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A319468 Number of partitions of n into exactly two nonzero decimal palindromes.

%I A319468 #12 Jan 10 2019 20:07:53
%S A319468 0,0,1,1,2,2,3,3,4,4,5,4,5,4,4,3,3,2,2,1,1,0,1,1,1,1,1,1,1,1,1,1,0,1,
%T A319468 1,1,1,1,1,1,1,1,1,0,2,1,1,1,1,1,1,1,1,1,0,2,1,1,1,1,1,1,1,1,1,0,3,1,
%U A319468 1,1,1,1,1,1,1,1,0,3,1,1,1,1,1,1,1,1,1
%N A319468 Number of partitions of n into exactly two nonzero decimal palindromes.
%H A319468 Alois P. Heinz, <a href="/A319468/b319468.txt">Table of n, a(n) for n = 0..10000</a>
%F A319468 a(n) = [x^n y^2] 1/Product_{j>=2} (1-y*x^A002113(j)).
%F A319468 a(n) = 0 <=> n in { A319477 }.
%p A319468 p:= proc(n) option remember; local i, s; s:= ""||n;
%p A319468       for i to iquo(length(s), 2) do if
%p A319468         s[i]<>s[-i] then return false fi od; true
%p A319468     end:
%p A319468 h:= proc(n) option remember; `if`(n<1, 0,
%p A319468      `if`(p(n), n, h(n-1)))
%p A319468     end:
%p A319468 b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i<n,
%p A319468       0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
%p A319468     end:
%p A319468 a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(2):
%p A319468 seq(a(n), n=0..100);
%Y A319468 Column k=2 of A319453.
%Y A319468 Cf. A002113, A319477.
%K A319468 nonn,look,base
%O A319468 0,5
%A A319468 _Alois P. Heinz_, Sep 19 2018