user2306: Electrum 2.0 and up uses BIP0032 internally. I want to write code that generates the same addresses. I can't find any information about this online.
What BIP32 paths does it use to generate addresses?

user60045: TL;DR:

BIP32 m/0/<n> path (receiving addresses)
BIP32 m/1/<n> path (change addresses)


Some days ago I had the very same question, so I ended writing this little nodejs module that does pretty much the same that you can read on @pedro_fp_simoes' answer:
https://www.npmjs.com/package/xpub-generator
You can use it as follows:
import { XPubGenerator } from 'xpub-generator';

const g = new XPubGenerator('xpub....');
g.nthReceiving(1);
g.nthChange(1);


user50631: Inspired by @NickODell answer, I created another example using nodejs that derives 5 receiving addresses and 5 change addresses.
You will need these two modules:
npm install bitcoinjs-lib --save
and
npm install bip32-utils --save
and babel for the es6 javascript code support.
import Bitcoin from 'bitcoinjs-lib';
import Bip32Utils from 'bip32-utils';

let hdNode = Bitcoin.HDNode.fromBase58('xpub...get.the.master.public.key.from.a.wallet.like.electrum...');

let receiving = hdNode.derive(0); // BIP32 m/0/<n> path (receiving addresses)
let receivingChain = new Bip32Utils.Chain(receiving);

for (var k = 0; k < 5; ++k) {
    console.log(receivingChain.get());
    receivingChain.next();
}

let change = hdNode.derive(1); // BIP32 m/1/<n> path (change addresses)
let changeChain = new Bip32Utils.Chain(change);

for (var k = 0; k < 5; ++k) {
    console.log(changeChain.get());
    changeChain.next();
}

Tested in electrum with a real wallet.
When you don't have a multiple account wallet you can use these BIP32 paths to generate addresses:
m/0/kcorresponds to the k'th keypair of the external chain of the HDW derived from master m.
m/1/k corresponds to the k'th keypair of the internal chain of the HDW derived from master m. (internal, means change and other internal uses)
But when you want to use a wallet with multiple accounts, for example, one for each customer, the paths are more like this:
m/i/0/k corresponds to the k'th keypair of the external chain of account number i of the HDW derived from master m.
m/i/1/k corresponds to the k'th keypair of the internal chain of account number i of the HDW derived from master m.
This is the default wallet layout:


user2306: It uses m/0/<n> for receiving addresses, and m/1/<n> for change addresses.
Here's some example bitcoinj code to generate receiving addresses from an extended public key.
String serialized_xpub = "xpub.....";
unsigned int address_num = 4;
NetworkParameters params = MainNetParams.get();
DeterministicKey root_xpub = DeterministicKey.deserializeB58(null, serialized_xpub, params);

DeterministicKey receiving = HDKeyDerivation.deriveChildKey(root_xpub, new ChildNumber(0, false));
DeterministicKey new_address_key = HDKeyDerivation.deriveChildKey(receiving, new ChildNumber(address_num, false));
String new_address = new_address_key.toAddress().toString();


2306: <p>Electrum 2.0 and up uses <a href="https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki">BIP0032</a> internally. I want to write code that generates the same addresses. I can't find any information about this online.</p>

<p>What BIP32 paths does it use to generate addresses?</p>
 60045: <p>TL;DR:</p>

<blockquote>
<pre><code>BIP32 m/0/&lt;n&gt; path (receiving addresses)
BIP32 m/1/&lt;n&gt; path (change addresses)
</code></pre>
</blockquote>

<p>Some days ago I had the very same question, so I ended writing this little nodejs module that does pretty much the same that you can read on @pedro_fp_simoes' answer:</p>

<p><a href="https://www.npmjs.com/package/xpub-generator" rel="nofollow noreferrer">https://www.npmjs.com/package/xpub-generator</a>
You can use it as follows:</p>

<pre><code>import { XPubGenerator } from 'xpub-generator';

const g = new XPubGenerator('xpub....');
g.nthReceiving(1);
g.nthChange(1);
</code></pre>
 50631: <p>Inspired by @NickODell answer, I created another example using nodejs that derives 5 receiving addresses and 5 change addresses.</p>

<p>You will need these two modules:
<code>npm install bitcoinjs-lib --save</code>
and
<code>npm install bip32-utils --save</code>
and <code>babel</code> for the <code>es6</code> javascript code support.</p>

<pre><code>import Bitcoin from 'bitcoinjs-lib';
import Bip32Utils from 'bip32-utils';

let hdNode = Bitcoin.HDNode.fromBase58('xpub...get.the.master.public.key.from.a.wallet.like.electrum...');

let receiving = hdNode.derive(0); // BIP32 m/0/&lt;n&gt; path (receiving addresses)
let receivingChain = new Bip32Utils.Chain(receiving);

for (var k = 0; k &lt; 5; ++k) {
    console.log(receivingChain.get());
    receivingChain.next();
}

let change = hdNode.derive(1); // BIP32 m/1/&lt;n&gt; path (change addresses)
let changeChain = new Bip32Utils.Chain(change);

for (var k = 0; k &lt; 5; ++k) {
    console.log(changeChain.get());
    changeChain.next();
}
</code></pre>

<p>Tested in electrum with a real wallet.</p>

<p>When you don't have a multiple account wallet you can use these BIP32 paths to generate addresses:</p>

<p><code>m/0/k</code>corresponds to the k'th keypair of the external chain of the HDW derived from master m.</p>

<p><code>m/1/k</code> corresponds to the k'th keypair of the internal chain of the HDW derived from master m. (internal, means change and other internal uses)</p>

<p>But when you want to use a wallet with multiple accounts, for example, one for each customer, the paths are more like this:</p>

<p><code>m/i/0/k</code> corresponds to the k'th keypair of the external chain of account number i of the HDW derived from master m.</p>

<p><code>m/i/1/k</code> corresponds to the k'th keypair of the internal chain of account number i of the HDW derived from master m.</p>

<p>This is the default wallet layout:</p>

<p><a href="https://i.stack.imgur.com/7jgkj.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/7jgkj.png" alt="Wallet structure"></a></p>
 2306: <p>It uses <code>m/0/&lt;n&gt;</code> for receiving addresses, and <code>m/1/&lt;n&gt;</code> for change addresses.</p>

<p>Here's some example bitcoinj code to generate receiving addresses from an extended public key.</p>

<pre><code>String serialized_xpub = "xpub.....";
unsigned int address_num = 4;
NetworkParameters params = MainNetParams.get();
DeterministicKey root_xpub = DeterministicKey.deserializeB58(null, serialized_xpub, params);

DeterministicKey receiving = HDKeyDerivation.deriveChildKey(root_xpub, new ChildNumber(0, false));
DeterministicKey new_address_key = HDKeyDerivation.deriveChildKey(receiving, new ChildNumber(address_num, false));
String new_address = new_address_key.toAddress().toString();
</code></pre>
