A247599 Number of ways of writing n as a sum: n = 2^0*k(0)^3 + 2^1*k(1)^3 + 2^2*k(2)^3 + ... where the k's are nonnegative integers.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 4, 2, 2, 2, 4, 3, 2, 2, 5, 4, 3, 3, 4, 3, 2, 2, 6, 4, 4, 4, 4, 3, 2, 3, 7, 5, 4, 4, 4, 3, 3, 4, 8, 5, 5, 6, 4, 4, 4, 4, 10, 6, 8, 7, 6, 5, 6, 5, 10, 5, 8, 7, 6, 4, 6, 4, 12, 8, 8, 8, 8, 7

Offset

0,9

Links

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

Maple

b:= proc(n, i) option remember; `if`(n=0, 1,
      `if`(n<0 or i<0, 0, add(b(n-2^i*j^3, i-1),
           j=0..iroot(iquo(n, 2^i), 3))))
    end:
a:= n-> b(n, ilog2(n)):
seq(a(n), n=0..100);  # Alois P. Heinz, Dec 28 2014

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1,
     If[n < 0 || i < 0, 0, Sum[b[n - 2^i*j^3, i - 1],
       {j, 0, Floor@Quotient[n, 2^i]^(1/3)}]]];
a[n_] := b[n, Floor@Log2[n]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, May 01 2022, after Alois P. Heinz *)

Crossrefs

Sequence in context: A354598 A239061 A309025 * A083897 A368212 A025823

Adjacent sequences: A247596 A247597 A247598 * A247600 A247601 A247602

Keyword

nonn,look

Author

David S. Newman, Sep 21 2014

Status

approved