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A319469 Number of partitions of n into exactly four nonzero decimal palindromes.

%I A319469 #8 Sep 28 2018 05:50:02
%S A319469 0,0,0,0,1,1,2,3,5,6,9,11,15,17,22,24,29,31,35,36,40,39,41,39,40,37,
%T A319469 37,33,33,29,28,25,25,22,22,21,21,20,20,20,20,20,20,20,20,20,21,21,22,
%U A319469 22,23,23,24,24,25,24,25,25,25,25,25,25,25,25,25,25,25,26
%N A319469 Number of partitions of n into exactly four nonzero decimal palindromes.
%H A319469 Alois P. Heinz, <a href="/A319469/b319469.txt">Table of n, a(n) for n = 0..10000</a>
%F A319469 a(n) = [x^n y^4] 1/Product_{j>=2} (1-y*x^A002113(j)).
%p A319469 p:= proc(n) option remember; local i, s; s:= ""||n;
%p A319469       for i to iquo(length(s), 2) do if
%p A319469         s[i]<>s[-i] then return false fi od; true
%p A319469     end:
%p A319469 h:= proc(n) option remember; `if`(n<1, 0,
%p A319469      `if`(p(n), n, h(n-1)))
%p A319469     end:
%p A319469 b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i<n,
%p A319469       0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
%p A319469     end:
%p A319469 a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(4):
%p A319469 seq(a(n), n=0..100);
%Y A319469 Column k=4 of A319453.
%Y A319469 Cf. A002113.
%K A319469 nonn,base,look
%O A319469 0,7
%A A319469 _Alois P. Heinz_, Sep 19 2018