A319472 Number of partitions of n into exactly seven nonzero decimal palindromes.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 21, 27, 37, 46, 60, 73, 91, 108, 131, 151, 178, 201, 231, 256, 287, 311, 342, 365, 393, 412, 437, 450, 470, 479, 493, 496, 505, 503, 508, 503, 504, 496, 496, 487, 487, 479, 478, 472, 473, 469, 472, 471, 476, 477

Offset

0,10

Links

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

Formula

a(n) = [x^n y^7] 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))(7):
seq(a(n), n=0..100);

Crossrefs

Column k=7 of A319453.

Cf. A002113.

Sequence in context: A260164 A280938 A049756 * A357660 A309099 A218507

Adjacent sequences: A319469 A319470 A319471 * A319473 A319474 A319475

Keyword

nonn,base,look

Author

Alois P. Heinz, Sep 19 2018

Status

approved