login
Number of partitions of n into exactly eight nonzero decimal palindromes.
4

%I #6 Sep 19 2018 17:09:42

%S 0,0,0,0,0,0,0,0,1,1,2,3,5,7,11,15,22,28,39,49,65,80,102,123,152,179,

%T 215,248,292,331,380,423,477,522,578,623,679,721,773,811,859,889,929,

%U 953,985,1000,1025,1032,1050,1051,1063,1060,1068,1062,1068,1062,1068

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

%H Alois P. Heinz, <a href="/A319473/b319473.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = [x^n y^8] 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))(8):

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

%Y Column k=8 of A319453.

%Y Cf. A002113.

%K nonn,base

%O 0,11

%A _Alois P. Heinz_, Sep 19 2018