A319471 Number of partitions of n into exactly six nonzero decimal palindromes.

0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 14, 20, 25, 34, 41, 53, 62, 76, 88, 104, 116, 134, 145, 163, 174, 189, 197, 211, 215, 225, 226, 232, 229, 233, 227, 228, 221, 219, 212, 211, 203, 201, 195, 194, 189, 190, 186, 187, 186, 188, 188, 192, 192, 197, 199, 204

Offset

0,9

Links

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

Formula

a(n) = [x^n y^6] 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))(6):
seq(a(n), n=0..100);

Crossrefs

Column k=6 of A319453.

Cf. A002113.

Sequence in context: A309097 A309098 A136185 * A218506 A238659 A341870

Adjacent sequences: A319468 A319469 A319470 * A319472 A319473 A319474

Keyword

nonn,base

Author

Alois P. Heinz, Sep 19 2018

Status

approved