A319474 Number of partitions of n into exactly nine nonzero decimal palindromes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 51, 68, 85, 109, 134, 167, 200, 244, 286, 341, 395, 460, 523, 600, 671, 756, 835, 926, 1008, 1103, 1185, 1280, 1360, 1450, 1524, 1609, 1673, 1748, 1803, 1867, 1910, 1965, 1996, 2039, 2063, 2096

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=9 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))(9):
seq(a(n), n=0..100);

Mathematica

Table[Count[IntegerPartitions[n,{9}],?(AllTrue[#,PalindromeQ]&)],{n,0,60}] (* _Harvey P. Dale, May 24 2025 *)

Formula

a(n) = [x^n y^9] 1/Product_{j>=2} (1-y*x^A002113(j)).