A319473 Number of partitions of n into exactly eight nonzero decimal palindromes.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 22, 28, 39, 49, 65, 80, 102, 123, 152, 179, 215, 248, 292, 331, 380, 423, 477, 522, 578, 623, 679, 721, 773, 811, 859, 889, 929, 953, 985, 1000, 1025, 1032, 1050, 1051, 1063, 1060, 1068, 1062, 1068, 1062, 1068

Offset

0,11

Links

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

Formula

a(n) = [x^n y^8] 1/Product_{j>=2} (1-y*x^A002113(j)).

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<n,
      0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
    end:
a:= n-> (k-> b(n, h(n), k)-b(n, h(n), k-1))(8):
seq(a(n), n=0..100);

Crossrefs

Column k=8 of A319453.

Cf. A002113.

Sequence in context: A307547 A182804 A242695 * A085894 A354468 A309194

Adjacent sequences: A319470 A319471 A319472 * A319474 A319475 A319476

Keyword

nonn,base

Author

Alois P. Heinz, Sep 19 2018

Status

approved