(35S) OEIS A000463 (N THEN N^2) & A 159693 (∑ A000463) Formula

[Gerald H]

OEIS sequence A000463, integers followed by square of integer

1, 1, 2, 4, 3, 9, 4, 16, 5, 25, 6, 36, 7, 49, 8, 64, 9, 81, 10, 100, 11, 121, 12, 144, 13, 169….

For positive integer N input solve this equation

G = IDIV( ( N+1 ) , 2 ) ^ ( 2 – ( RMDR( N , 2 ) ► R ) ) + 0 * ( ( N * ( SQ( N ) + 3 * N + 8 ) + ( 3 * N + 9 ) * R + 3 * SQ( N ) * ( 1 – R ) ) / 24 ► S )

for G. You will be prompted for values other than N, ignore these prompts with R/S.

eg

For N=1953

The calculator returns

G=977.

In variable S you find the sum of the first 1953 terms

S=310,858,929