Formula For Finding the Next Near Consecutive Perfect Square For any three consecutive members of a sequence, the first and third members are near consecutive.
1 squared is 1. 2 squared is 4. So 1 and 4 are consecutive perfect squares.
1 squared is 1. 3 squared is 9. So 1 and 9 are near consecutive perfect squares.
I want to verify this formula to go from any perfect square to the next near consecutive perfect square. Let a be any perfect square. Let c be the next near consecutive perfect square. Here is the formula:
a+4(1+$\sqrt a$)=c
Example:
49+4(1+$\sqrt 49$)=81
Did I get the formula right? Is my terminology ok?

Actually the next near perfect square would be $64$. A better formula $a + 2(a)^{\frac12}+1 = c$
Example being:
$$49 + 2(49)^{\frac12} + 1 = 64$$
$$49 + 2(7) + 1 = 64$$
$$49 + 14 + 1 = 64$$
$$64=64$$
