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

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

A column of A072170.

Programs

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 *)

Formula

G.f.: Product_{k>=0} (1 - x^(7*2^k))/(1 - x^(2^k)). - Ilya Gutkovskiy, Jul 09 2019

Extensions

More terms from Vladeta Jovovic, May 07 2004