A341166 - OEIS

%I #8 Feb 06 2021 14:27:09

%S 1,1,1,2,2,3,3,4,4,4,4,4,3,3,3,3,3,3,4,4,6,7,8,8,10,10,11,11,11,11,11,

%T 11,11,11,10,11,11,11,11,11,12,12,13,14,15,16,19,20,22,24,25,27,28,29,

%U 29,30,29,31,30,30,30,30,31,31,32,33,34,35,39,39

%N Number of partitions of n into 8 distinct nonzero decimal palindromes.

%H Alois P. Heinz, <a href="/A341166/b341166.txt">Table of n, a(n) for n = 36..20000</a>

%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-1)), 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=36..105);  # _Alois P. Heinz_, Feb 06 2021

%Y Cf. A002113, A136522, A319473, A341155, A341156, A341157, A341158, A341159, A341165, A341167, A341168.

%K nonn,base

%O 36,4

%A _Ilya Gutkovskiy_, Feb 06 2021