A319474 Number of partitions of n into exactly nine nonzero decimal palindromes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 51, 68, 85, 109, 134, 167, 200, 244, 286, 341, 395, 460, 523, 600, 671, 756, 835, 926, 1008, 1103, 1185, 1280, 1360, 1450, 1524, 1609, 1673, 1748, 1803, 1867, 1910, 1965, 1996, 2039, 2063, 2096

Offset

0,12

Links

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

Formula

a(n) = [x^n y^9] 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))(9):
seq(a(n), n=0..100);

Crossrefs

Column k=9 of A319453.

Cf. A002113.

Sequence in context: A354468 A309194 A330640 * A218508 A340719 A026814

Adjacent sequences: A319471 A319472 A319473 * A319475 A319476 A319477

Keyword

nonn,base

Author

Alois P. Heinz, Sep 19 2018

Status

approved