A256855 Number of ordered ways to write n as x*(3*x-1)/2 + y*(3*y+1)/2 + z*(3*z+1), where x and y are nonnegative integers and z is an integer.
1, 1, 2, 2, 2, 3, 1, 4, 1, 3, 2, 3, 4, 1, 4, 3, 5, 4, 3, 3, 2, 3, 5, 1, 5, 2, 7, 3, 3, 6, 4, 7, 3, 4, 2, 3, 4, 7, 4, 5, 4, 6, 5, 3, 5, 6, 4, 4, 3, 4, 5, 8, 8, 4, 5, 6, 5, 5, 4, 7, 5, 6, 7, 3, 7, 4, 7, 5, 6, 2, 5, 8, 10, 3, 4, 6, 6, 7, 4, 9, 5, 10, 10, 5, 4, 6, 6, 8, 4, 8, 3, 6, 11, 5, 8, 4, 10, 4, 2, 8, 5
Offset: 0
Keywords
Examples
a(8) = 1 since 8 = 1*(3*1-1)/2 + 2*(3*2+1)/2 + 0*(3*0+1). a(23) = 1 since 23 = 3*(3*3-1)/2 + 2*(3*2+1)/2 + 1*(3*1+1).
Links
- Zhi-Wei Sun, Table of n, a(n) for n = 0..10000
- Zhi-Wei Sun, On universal sums of polygonal numbers, arXiv:0905.0635 [math.NT], 2009-2015.
Programs
-
Mathematica
PQ[n_]:=IntegerQ[Sqrt[12n+1]] Do[r=0;Do[If[PQ[n-x(3x-1)/2-y(3y+1)/2],r=r+1],{x,0,(Sqrt[24n+1]+1)/6},{y,0,(Sqrt[24(n-x(3x-1)/2)+1]-1)/6}]; Print[n," ",r];Continue,{n,0,100}]
Comments