A094765 a(n) = n + 2 * square excess of n.

0, 1, 4, 7, 4, 7, 10, 13, 16, 9, 12, 15, 18, 21, 24, 27, 16, 19, 22, 25, 28, 31, 34, 37, 40, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91

Offset: 0

Author

N. J. A. Sloane, Jun 10 2004

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• S. H. Weintraub, An interesting recursion, Amer. Math. Monthly, 111 (No. 6, 2004), 528-530.

Crossrefs

Cf. A002061, A053186, A094766.

Programs

Maple

seq(3*n - 2*floor(sqrt(n))^2, n=0..1000); # Robert Israel, Oct 23 2015

PARI

a(n) = 3*n - 2*sqrtint(n)^2; \\ Michel Marcus, Oct 23 2015

Formula

a(n) = n + 2*A053186(n).

G.f.: 3*x/(1-x)^2 - (2/(1-x)) * Sum_{k>=1} (2*k-1)*x^(k^2). The sum is related to Jacobi theta functions. - Robert Israel, Oct 23 2015