A319454 Number of partitions of 2n into exactly n nonzero decimal palindromes.

1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 41, 53, 72, 92, 121, 153, 197, 245, 310, 381, 475, 579, 711, 858, 1043, 1248, 1501, 1783, 2126, 2507, 2966, 3476, 4083, 4757, 5551, 6433, 7464, 8606, 9931, 11398, 13089, 14957, 17099, 19461, 22153, 25120, 28483, 32183, 36361

Offset: 0

Author

Alois P. Heinz, Sep 19 2018

Keywords

• nonn
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1500

Crossrefs

Cf. A002113, A319453.

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`(i<1 or
      t<1, 0, b(n, h(i-1), t)+b(n-i, h(min(n-i, i)), t-1)))
    end:
a:= n-> `if`(n=0, 1, b(2*n, h(2*n), n)-b(2*n, h(2*n), n-1)):
seq(a(n), n=0..70);

Formula

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

a(n) = A319453(2n,n).