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A276431 Number of partitions of n containing no parts that are powers of 2 with positive exponent. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 30 02:40 EST 2023. Contains 359939 sequences. (Running on oeis4.)