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