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A007728 5th binary partition function. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

Sequence in context: A070803 A071693 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

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Last modified November 17 01:05 EST 2019. Contains 329209 sequences. (Running on oeis4.)