A319922 Number of ways of writing n as a sum of exactly 10 powers of 2.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 5, 6, 6, 7, 8, 9, 8, 10, 9, 10, 11, 13, 11, 14, 12, 13, 12, 15, 12, 16, 14, 16, 14, 18, 15, 19, 17, 21, 18, 22, 17, 22, 18, 22, 19, 25, 19, 24, 20, 25, 21, 28, 21, 27, 21, 26, 19, 27, 20, 26, 19

Offset

0,14

Links

Alois P. Heinz, Table of n, a(n) for n = 0..65536

Formula

a(n) = [x^n y^10] 1/Product_{j>=0} (1-y*x^(2^j)).

Maple

h:= proc(n) option remember; `if`(n<1, 0,
      `if`(n=2^ilog2(n), n, h(n-1)))
    end:
b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0), `if`(
      k>n or i*k<n, 0, b(n, h(i-1), k)+b(n-i, h(min(n-i, i)), k-1)))
    end:
a:= n-> b(n, h(n), 10):
seq(a(n), n=0..120);

Crossrefs

Column k=10 of A089052.

Cf. A000079.

Sequence in context: A063124 A358901 A070547 * A289139 A094838 A025768

Adjacent sequences: A319919 A319920 A319921 * A319923 A319924 A319925

Keyword

nonn,look

Author

Alois P. Heinz, Oct 01 2018

Status

approved