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A319475 Number of partitions of n into exactly ten nonzero decimal palindromes. 4

%I #6 Sep 19 2018 17:10:23

%S 0,0,0,0,0,0,0,0,0,0,1,1,2,3,5,7,11,15,22,29,41,52,70,88,114,141,178,

%T 215,265,315,380,445,526,606,705,801,916,1027,1159,1282,1427,1561,

%U 1715,1855,2015,2157,2318,2458,2614,2747,2897,3018,3157,3266,3390,3485

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

%H Alois P. Heinz, <a href="/A319475/b319475.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = [x^n y^10] 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))(10):

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

%Y Column k=10 of A319453.

%Y Cf. A002113.

%K nonn,base

%O 0,13

%A _Alois P. Heinz_, Sep 19 2018

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)