A319470 Number of partitions of n into exactly five nonzero decimal palindromes.

0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 10, 13, 18, 22, 29, 34, 42, 48, 57, 63, 72, 77, 85, 88, 95, 96, 100, 99, 101, 98, 98, 93, 92, 87, 85, 80, 79, 74, 73, 70, 69, 67, 67, 65, 66, 65, 66, 66, 67, 68, 69, 70, 72, 73, 75, 76, 78, 79, 81, 81, 83, 83, 84, 84, 85, 84

Offset: 0

Author

Alois P. Heinz, Sep 19 2018

Keywords

• nonn
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Column k=5 of A319453.

Cf. A002113.

Programs

Maple

p:= proc(n) option remember; local i, s; s:= ""||n;
      for i to iquo(length(s), 2) do if
        s[i]<>s[-i] then return false fi od; true
    end:
h:= proc(n) option remember; `if`(n<1, 0,
     `if`(p(n), n, h(n-1)))
    end:
b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(t*i (k-> b(n, h(n), k)-b(n, h(n), k-1))(5):
seq(a(n), n=0..100);

Mathematica

Table[Count[IntegerPartitions[n,{5}],?(AllTrue[#,PalindromeQ]&)],{n,0,70}] (* _Harvey P. Dale, Oct 20 2024 *)

Formula

a(n) = [x^n y^5] 1/Product_{j>=2} (1-y*x^A002113(j)).