A319468 Number of partitions of n into exactly two nonzero decimal palindromes.

0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 4, 5, 4, 4, 3, 3, 2, 2, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,5

Links

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

Formula

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

a(n) = 0 <=> n in { A319477 }.

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))(2):
seq(a(n), n=0..100);

Crossrefs

Column k=2 of A319453.

Cf. A002113, A319477.

Sequence in context: A336430 A368086 A167232 * A137791 A351834 A096125

Adjacent sequences: A319465 A319466 A319467 * A319469 A319470 A319471

Keyword

nonn,look,base

Author

Alois P. Heinz, Sep 19 2018

Status

approved