A093518 Number of ways of representing n as the sum of two (not necessarily distinct) generalized pentagonal numbers.

1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 0, 2, 1, 2, 1, 1, 2, 0, 1, 1, 0, 2, 1, 2, 0, 1, 3, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 0, 2, 2, 2, 0, 1, 1, 0, 2, 1, 0, 1, 1, 3, 1, 0, 1, 1, 2, 2, 1, 0, 1, 2, 1, 1, 0, 2, 0, 0, 1, 2, 1, 2, 1, 0, 2, 0, 3, 1, 2, 1, 0, 2, 1, 1, 1, 1, 0, 0, 1, 0, 1, 4, 1, 1, 0, 1, 2, 0, 2, 1, 1, 2, 1

Offset: 0

Author

Jon Perry, Mar 29 2004

Keywords

• nonn

Examples

			a(7)=2 as we have 7+0 = 5+2.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001318 (generalized pentagonal numbers), A093519 (where a(n)=0).

Programs

Maple

GP:= [0,seq(op([m*(3*m-1)/2, m*(3*m+1)/2]),m=1..11)]:
V:= Array(0..200):
for i from 1 to 23 do
  for j from 1 to i do
    r:= GP[i]+GP[j];
    if r > 200 then break fi;
    V[r]:= V[r]+1
od od:
convert(V,list); # Robert Israel, Feb 26 2025

PARI

{ v=vector(101); v[1]=0; for (i=1,50, v[2*i]=i*(3*i-1)/2; v[2*i+1]=i*(3*i+1)/2); x=vector(500); for (a=1,50, for (b=a,50, if (v[a]+v[b]<500, x[v[a]+v[b]+1]++))); x }

Extensions

Definition clarified by Robert Israel, Feb 26 2025