

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



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
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OFFSET

0,2


LINKS

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


FORMULA

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


EXAMPLE

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.


MAPLE

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


PROG

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


CROSSREFS

Cf. A000217, A001652, A049777, A049780.
Sequence in context: A106441 A131836 A133829 * A230296 A278317 A086454
Adjacent sequences: A160648 A160649 A160650 * A160652 A160653 A160654


KEYWORD

nonn


AUTHOR

Leroy Quet, May 21 2009


EXTENSIONS

Extended by Ray Chandler, Jun 16 2009


STATUS

approved



