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%I #22 May 28 2018 10:42:37
%S 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,
%T 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,
%U 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
%N 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.
%H Alois P. Heinz, <a href="/A160651/b160651.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) == 1 (mod 2) <=> n in { A001652 }. - _Alois P. Heinz_, May 27 2018
%e 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.
%p a:= n-> add(`if`(issqr(4*(n+m+1)*(n-m)+1), 1, 0), m=0..n):
%p seq(a(n), n=0..100); # _Alois P. Heinz_, May 27 2018
%o (PARI) a(n) = sum(m=0, n, ispolygonal(n*(n+1)/2 - m*(m+1)/2, 3)); \\ _Michel Marcus_, May 27 2018
%Y Cf. A000217, A001652, A049777, A049780.
%K nonn
%O 0,2
%A _Leroy Quet_, May 21 2009
%E Extended by _Ray Chandler_, Jun 16 2009
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