A076816 Squares modulo triangular numbers: n^2 minus the greatest triangular number smaller than or equal to n^2.

0, 0, 1, 3, 1, 4, 0, 4, 9, 3, 9, 1, 8, 16, 6, 15, 3, 13, 24, 10, 22, 6, 19, 1, 15, 30, 10, 26, 4, 21, 39, 15, 34, 8, 28, 0, 21, 43, 13, 36, 4, 28, 53, 19, 45, 9, 36, 64, 26, 55, 15, 45, 3, 34, 66, 22, 55, 9, 43, 78, 30, 66, 16, 53, 1, 39, 78, 24, 64, 8, 49, 91, 33, 76, 16, 60, 105, 43

Offset: 0

Author

Floor van Lamoen, Oct 17 2002

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A064784.

Programs

Maple

seq(n^2-floor(sqrt(2*n^2+1/4)-1/2)*floor(sqrt(2*n^2+1/4)+1/2)/2,n=0..100);

Mathematica

smt[n_]:=Module[{x=Floor[(Sqrt[1+8n]-1)/2]},n-(x(x+1))/2]; smt/@(Range[ 0,80]^2) (* Harvey P. Dale, May 12 2014 *)

Formula

a(n)=n^2-floor(sqrt(2*n^2+1/4)-1/2)*floor(sqrt(2*n^2+1/4)+1/2)/2