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

0,3

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.

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

Maple

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

Prog

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

Crossrefs

Cf. A002061, A053186, A094766.

Sequence in context: A254398 A081884 A059143 * A170863 A021682 A242187

Adjacent sequences: A094762 A094763 A094764 * A094766 A094767 A094768

Keyword

nonn

Author

N. J. A. Sloane, Jun 10 2004

Status

approved