A319472 Number of partitions of n into exactly seven nonzero decimal palindromes.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 21, 27, 37, 46, 60, 73, 91, 108, 131, 151, 178, 201, 231, 256, 287, 311, 342, 365, 393, 412, 437, 450, 470, 479, 493, 496, 505, 503, 508, 503, 504, 496, 496, 487, 487, 479, 478, 472, 473, 469, 472, 471, 476, 477

Offset: 0

Author

Alois P. Heinz, Sep 19 2018

Keywords

• nonn
• base
• look

Links

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

Crossrefs

Column k=7 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))(7):
seq(a(n), n=0..100);

Formula

a(n) = [x^n y^7] 1/Product_{j>=2} (1-y*x^A002113(j)).