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

0,3

Links

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

Formula

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

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

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);

Crossrefs

Cf. A002113, A319453.

Sequence in context: A238866 A035978 A319475 * A023029 A358909 A035987

Adjacent sequences: A319451 A319452 A319453 * A319455 A319456 A319457

Keyword

nonn,base

Author

Alois P. Heinz, Sep 19 2018

Status

approved