cp's OEIS Frontend

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

%I A093518 #15 Feb 27 2025 08:26:13
%S A093518 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,
%T A093518 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,
%U A093518 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
%N A093518 Number of ways of representing n as the sum of two (not necessarily distinct) generalized pentagonal numbers.
%H A093518 Robert Israel, <a href="/A093518/b093518.txt">Table of n, a(n) for n = 0..10000</a>
%e A093518 a(7)=2 as we have 7+0 = 5+2.
%p A093518 GP:= [0,seq(op([m*(3*m-1)/2, m*(3*m+1)/2]),m=1..11)]:
%p A093518 V:= Array(0..200):
%p A093518 for i from 1 to 23 do
%p A093518   for j from 1 to i do
%p A093518     r:= GP[i]+GP[j];
%p A093518     if r > 200 then break fi;
%p A093518     V[r]:= V[r]+1
%p A093518 od od:
%p A093518 convert(V,list); # _Robert Israel_, Feb 26 2025
%o A093518 (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 }
%Y A093518 Cf. A001318 (generalized pentagonal numbers), A093519 (where a(n)=0).
%K A093518 nonn
%O A093518 0,3
%A A093518 _Jon Perry_, Mar 29 2004
%E A093518 Definition clarified by _Robert Israel_, Feb 26 2025