A007728 5th binary partition function.

1, 1, 2, 2, 4, 3, 5, 4, 8, 6, 9, 7, 12, 8, 12, 9, 17, 12, 18, 14, 23, 15, 22, 16, 28, 19, 27, 20, 32, 20, 29, 21, 38, 26, 38, 29, 47, 30, 44, 32, 55, 37, 52, 38, 60, 37, 53, 38, 66, 44, 63, 47, 74, 46, 66, 47, 79, 52, 72, 52, 81, 49, 70, 50, 88, 59, 85, 64

Offset

0,3

Comments

The number of ways of writing n as a sum of powers of 2, each power being used at most four times. - Dmitry Kamenetsky, Jul 14 2023

Links

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

B. Reznick, Some binary partition functions, in "Analytic number theory" (Conf. in honor P. T. Bateman, Allerton Park, IL, 1989), 451-477, Progr. Math., 85, Birkhäuser Boston, Boston, MA, 1990.

Formula

G.f.: Product_{k>=0} (1 - x^(5*2^k))/(1 - x^(2^k)). - Ilya Gutkovskiy, Jul 09 2019

Maple

b:= proc(n, i) option remember;
      `if`(n=0, 1, `if`(i<0, 0, add(`if`(n-j*2^i<0, 0,
         b(n-j*2^i, i-1)), j=0..4)))
    end:
a:= n-> b(n, ilog2(n)):
seq(a(n), n=0..70);  # Alois P. Heinz, Jun 21 2012

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 0, 0, Sum[If[n-j*2^i < 0, 0, b[n-j*2^i, i-1, k]], {j, 0, k-1}]]]; a[n_] := b[n, Log[2, n] // Floor, 5]; Table[a[n], {n, 0, 70} ] (* Jean-François Alcover, Jan 17 2014, after Alois P. Heinz *)

Crossrefs

A column of A072170.

Cf. A000123, A018819.

Sequence in context: A071693 A372825 A225381 * A262991 A077026 A060026

Adjacent sequences: A007725 A007726 A007727 * A007729 A007730 A007731

Keyword

nonn,look

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, May 06 2004

Status

approved