A276431 Number of partitions of n containing no parts that are powers of 2 with positive exponent.

1, 1, 1, 2, 2, 3, 5, 6, 7, 10, 13, 16, 22, 27, 33, 43, 52, 64, 81, 98, 120, 148, 178, 215, 263, 315, 377, 455, 541, 644, 771, 912, 1078, 1279, 1506, 1772, 2089, 2447, 2864, 3356, 3916, 4563, 5320, 6180, 7171, 8324, 9633, 11136, 12874, 14845, 17102, 19696

Offset: 0

Author

Emeric Deutsch, Sep 19 2016

Keywords

• nonn

Examples

			a(6) = 5, counting [1,1,1,1,1,1], [1,1,1,3], [1,5], [3,3], [6].
		

Links

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

Crossrefs

Cf. A276430.

Programs

Maple

h:= proc(i) options operator, arrow: 2^i end proc: g := product((1-x^h(i))/(1-x^i), i = 1 .. 55): gser := series(g, x = 0, 55): seq(coeff(gser, x, n), n = 0 .. 50);
# second Maple program:
with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(`if`(d>1 and
      d=2^ilog2(d), 0, a(n-j)*d), d=divisors(j)), j=1..n)/n)
    end:
seq(a(n), n=0..55);  # Alois P. Heinz, Sep 20 2016

Mathematica

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[If[d>1 && d == 2^Floor[Log[2, d]], 0, a[n-j]*d], {d, Divisors[j]}], {j, 1, n}]/n]; Table[a[n], {n, 0, 55}] (* Jean-François Alcover, Dec 21 2016, after Alois P. Heinz *)

Formula

a(n) = A276430(n,0).

G.f.: g(x) = Product_{i>=1} (1-x^{h(i)})/(1-x^i), where h(i) = 2^i.