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

0,3

Links

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

Example

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

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

Prog

(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 }

Crossrefs

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

Sequence in context: A238988 A261013 A335106 * A128184 A373244 A025450

Adjacent sequences: A093515 A093516 A093517 * A093519 A093520 A093521

Keyword

nonn

Author

Jon Perry, Mar 29 2004

Extensions

Definition clarified by Robert Israel, Feb 26 2025

Status

approved