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A319469 Number of partitions of n into exactly four nonzero decimal palindromes. 2

%I

%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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Last modified March 19 19:45 EDT 2019. Contains 321331 sequences. (Running on oeis4.)