A112367 a(n) = A000217(n-k), where k is the largest triangular number less than n.

0, 0, 1, 0, 1, 3, 0, 1, 3, 6, 0, 1, 3, 6, 10, 0, 1, 3, 6, 10, 15, 0, 1, 3, 6, 10, 15, 21, 0, 1, 3, 6, 10, 15, 21, 28, 0, 1, 3, 6, 10, 15, 21, 28, 36, 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 0, 1, 3, 6, 10

Offset: 0

Author

Amarnath Murthy, Sep 12 2005

Keywords

• easy
• nonn

Examples

			a(9) = T(9-6) = T(3) = 6. 6 < 9 < 10.
		

Programs

Maple

A112367 := proc(n)
        t := A057944(n) ;
        A000217(n-t) ;
end proc:
seq(A112367(n),n=0..80) ; # R. J. Mathar, Nov 05 2011

Mathematica

trn[n_]:=Module[{c=Floor[(Sqrt[8n+1]-1)/2],x},x=n-(c(c+1))/2;(x(x+1))/2]; Array[trn,80,0] (* Harvey P. Dale, Jul 19 2012 *)

Formula

a(n) = A000217(n-A057944(n)). - R. J. Mathar, Nov 05 2011