A319469 Number of partitions of n into exactly four nonzero decimal palindromes.

0, 0, 0, 0, 1, 1, 2, 3, 5, 6, 9, 11, 15, 17, 22, 24, 29, 31, 35, 36, 40, 39, 41, 39, 40, 37, 37, 33, 33, 29, 28, 25, 25, 22, 22, 21, 21, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26

Offset

0,7

Links

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

Formula

a(n) = [x^n y^4] 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))(4):
seq(a(n), n=0..100);

Crossrefs

Column k=4 of A319453.

Cf. A002113.

Sequence in context: A123399 A239010 A104738 * A341123 A365877 A325863

Adjacent sequences: A319466 A319467 A319468 * A319470 A319471 A319472

Keyword

nonn,base,look

Author

Alois P. Heinz, Sep 19 2018

Status

approved