A319475 Number of partitions of n into exactly ten nonzero decimal palindromes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 41, 52, 70, 88, 114, 141, 178, 215, 265, 315, 380, 445, 526, 606, 705, 801, 916, 1027, 1159, 1282, 1427, 1561, 1715, 1855, 2015, 2157, 2318, 2458, 2614, 2747, 2897, 3018, 3157, 3266, 3390, 3485

Offset

0,13

Links

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

Formula

a(n) = [x^n y^10] 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))(10):
seq(a(n), n=0..100);

Crossrefs

Column k=10 of A319453.

Cf. A002113.

Sequence in context: A347574 A238866 A035978 * A319454 A023029 A358909

Adjacent sequences: A319472 A319473 A319474 * A319476 A319477 A319478

Keyword

nonn,base

Author

Alois P. Heinz, Sep 19 2018

Status

approved