%I #24 Dec 09 2024 15:55:13
%S 1,1,1,1,2,1,2,1,1,2,1,2,1,1,2,1,2,1,1,2,1,2,1,2,1,1,2,1,2,1,1,2,1,2,
%T 1,2,1,1,2,1,2,1,1,2,1,2,1,1,2,1,2,1,2,1,1,2,1,2,1,1,2,1,2,1,2,1,1,2,
%U 1,2,1,1,2,1,2,1,1,2,1,2,1,2,1,1,2,1,2,1,1,2,1,2,1,2,1,1,2,1,2,1,1,2,1,2,1,1
%N Number of triangular numbers in interval ](n-1)^2, n^2] for n>0, a(0)=1.
%H Alois P. Heinz, <a href="/A214856/b214856.txt">Table of n, a(n) for n = 0..10000</a>
%e 10, 15 are in interval ]9, 16] , a(4) = 2.
%o (PARI) a(n) = if (n, sum(i=(n-1)^2+1, n^2, ispolygonal(i, 3)), 1); \\ _Michel Marcus_, Nov 12 2022
%o (Python)
%o from math import isqrt
%o def A214856(n): return (isqrt((m:=n**2<<3)+8)+1>>1)-(isqrt(m-(n-1<<4))+1>>1) if n else 1 # _Chai Wah Wu_, Dec 09 2024
%Y Cf. A000217, A000290, A214848, A214857.
%K nonn,easy
%O 0,5
%A _Philippe Deléham_, Mar 08 2013