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

%I #6 Sep 19 2018 17:08:44

%S 0,0,0,0,0,0,1,1,2,3,5,7,11,14,20,25,34,41,53,62,76,88,104,116,134,

%T 145,163,174,189,197,211,215,225,226,232,229,233,227,228,221,219,212,

%U 211,203,201,195,194,189,190,186,187,186,188,188,192,192,197,199,204

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

%H Alois P. Heinz, <a href="/A319471/b319471.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = [x^n y^6] 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))(6):

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

%Y Column k=6 of A319453.

%Y Cf. A002113.

%K nonn,base

%O 0,9

%A _Alois P. Heinz_, Sep 19 2018