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

0,4

Links

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

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.

Example

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

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 *)

Crossrefs

Cf. A276430.

Sequence in context: A266746 A096981 A281966 * A308272 A035541 A187502

Adjacent sequences: A276428 A276429 A276430 * A276432 A276433 A276434

Keyword

nonn

Author

Emeric Deutsch, Sep 19 2016

Status

approved