A007730 7th binary partition function.

1, 1, 2, 2, 4, 4, 6, 5, 9, 8, 12, 10, 16, 14, 19, 15, 24, 20, 28, 22, 34, 29, 39, 30, 46, 38, 52, 40, 59, 49, 64, 48, 72, 58, 78, 59, 87, 72, 94, 70, 104, 84, 113, 85, 124, 102, 132, 98, 144, 115, 153, 114, 166, 136, 176, 130, 189, 151, 200, 148, 212, 172, 220

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^(7*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..6)))
    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, Length[IntegerDigits[n, 2]] - 1, 7];
Table[a[n], {n, 0, 70} ] (* Jean-François Alcover, Jan 17 2014, after Alois P. Heinz *)

Crossrefs

A column of A072170.

Sequence in context: A069345 A341948 A347661 * A330271 A257686 A057144

Adjacent sequences: A007727 A007728 A007729 * A007731 A007732 A007733

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, May 07 2004

Status

approved