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A341166 Number of partitions of n into 8 distinct nonzero decimal palindromes.

%I A341166 #8 Feb 06 2021 14:27:09
%S A341166 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 A341166 11,11,11,10,11,11,11,11,11,12,12,13,14,15,16,19,20,22,24,25,27,28,29,
%U A341166 29,30,29,31,30,30,30,30,31,31,32,33,34,35,39,39
%N A341166 Number of partitions of n into 8 distinct nonzero decimal palindromes.
%H A341166 Alois P. Heinz, <a href="/A341166/b341166.txt">Table of n, a(n) for n = 36..20000</a>
%p A341166 p:= proc(n) option remember; local i, s; s:= ""||n;
%p A341166       for i to iquo(length(s), 2) do if
%p A341166         s[i]<>s[-i] then return false fi od; true
%p A341166     end:
%p A341166 h:= proc(n) option remember; `if`(n<1, 0,
%p A341166      `if`(p(n), n, h(n-1)))
%p A341166     end:
%p A341166 b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i<n,
%p A341166       0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i-1)), t-1)))
%p A341166     end:
%p A341166 a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(8):
%p A341166 seq(a(n), n=36..105);  # _Alois P. Heinz_, Feb 06 2021
%Y A341166 Cf. A002113, A136522, A319473, A341155, A341156, A341157, A341158, A341159, A341165, A341167, A341168.
%K A341166 nonn,base
%O A341166 36,4
%A A341166 _Ilya Gutkovskiy_, Feb 06 2021