A160651 a(n) is the number of triangular nonnegative integers that are each equal to n(n+1)/2 - m(m+1)/2, for some m's where 0 <= m <= n.

1, 2, 2, 3, 2, 2, 4, 2, 4, 2, 4, 4, 2, 4, 2, 4, 4, 2, 4, 2, 3, 6, 2, 8, 2, 2, 4, 4, 8, 2, 2, 4, 2, 4, 2, 2, 8, 4, 4, 2, 4, 8, 2, 4, 4, 4, 6, 2, 4, 6, 2, 4, 4, 6, 4, 4, 4, 4, 6, 4, 2, 8, 4, 4, 4, 2, 8, 4, 4, 2, 2, 6, 2, 4, 4, 4, 4, 4, 12, 2, 4, 4, 2, 4, 2, 2, 8, 2, 8, 4, 2, 8, 4, 8, 4, 8, 8, 2, 4, 2, 2, 8, 2, 6, 2

Offset: 0

Author

Leroy Quet, May 21 2009

Keywords

• nonn

Examples

			For n = 6, the values of n(n+1)/2 - m(m+1)/2, 0 <= m <= n, are 21, 20, 18, 15, 11, 6, and 0. Of these, 21, 15, 6, and 0 are triangular numbers, so a(6) = 4.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000217, A001652, A049777, A049780.

Programs

Maple

a:= n-> add(`if`(issqr(4*(n+m+1)*(n-m)+1), 1, 0), m=0..n):
seq(a(n), n=0..100);  # Alois P. Heinz, May 27 2018

PARI

a(n) = sum(m=0, n, ispolygonal(n*(n+1)/2 - m*(m+1)/2, 3)); \\ Michel Marcus, May 27 2018

Formula

a(n) == 1 (mod 2) <=> n in { A001652 }. - Alois P. Heinz, May 27 2018

Extensions

Extended by Ray Chandler, Jun 16 2009