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A319468 Number of partitions of n into exactly two nonzero decimal palindromes. 6

%I #12 Jan 10 2019 20:07:53

%S 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 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 1,1,1,1,1,1,1,1,0,3,1,1,1,1,1,1,1,1,1

%N Number of partitions of n into exactly two nonzero decimal palindromes.

%H Alois P. Heinz, <a href="/A319468/b319468.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = [x^n y^2] 1/Product_{j>=2} (1-y*x^A002113(j)).

%F a(n) = 0 <=> n in { A319477 }.

%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))(2):

%p seq(a(n), n=0..100);

%Y Column k=2 of A319453.

%Y Cf. A002113, A319477.

%K nonn,look,base

%O 0,5

%A _Alois P. Heinz_, Sep 19 2018

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)