A319470 Number of partitions of n into exactly five nonzero decimal palindromes.

0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 10, 13, 18, 22, 29, 34, 42, 48, 57, 63, 72, 77, 85, 88, 95, 96, 100, 99, 101, 98, 98, 93, 92, 87, 85, 80, 79, 74, 73, 70, 69, 67, 67, 65, 66, 65, 66, 66, 67, 68, 69, 70, 72, 73, 75, 76, 78, 79, 81, 81, 83, 83, 84, 84, 85, 84

Offset

0,8

Links

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

Formula

a(n) = [x^n y^5] 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))(5):
seq(a(n), n=0..100);

Mathematica

Table[Count[IntegerPartitions[n, {5}], _?(AllTrue[#, PalindromeQ]&)], {n, 0, 70}] (* Harvey P. Dale, Oct 20 2024 *)

Crossrefs

Column k=5 of A319453.

Cf. A002113.

Sequence in context: A282569 A372618 A213213 * A115001 A349060 A338380

Adjacent sequences: A319467 A319468 A319469 * A319471 A319472 A319473

Keyword

nonn,base

Author

Alois P. Heinz, Sep 19 2018

Status

approved