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A339426 Number of compositions (ordered partitions) of n into an even number of powers of 2. 1
1, 0, 1, 2, 2, 6, 9, 14, 30, 48, 86, 156, 268, 478, 849, 1486, 2638, 4660, 8214, 14532, 25664, 45304, 80078, 141412, 249768, 441276, 779376, 1376696, 2431924, 4295534, 7587753, 13403102, 23674870, 41819588, 73870046, 130483396, 230486384, 407130332, 719153726 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..38.

Index entries for sequences related to compositions

FORMULA

G.f.: (1/2) * (1 / (1 - Sum_{k>=0} x^(2^k)) + 1 / (1 + Sum_{k>=0} x^(2^k))).

a(n) = (A023359(n) + A339422(n)) / 2.

a(n) = Sum_{k=0..n} A023359(k) * A339422(n-k).

EXAMPLE

a(5) = 6 because we have [4, 1], [1, 4], [2, 1, 1, 1], [1, 2, 1, 1], [1, 1, 2, 1] and [1, 1, 1, 2].

MAPLE

b:= proc(n, t) option remember; `if`(n=0, t,

      add(b(n-2^i, 1-t), i=0..ilog2(n)))

    end:

a:= n-> b(n, 1):

seq(a(n), n=0..42);  # Alois P. Heinz, Dec 03 2020

MATHEMATICA

nmax = 38; CoefficientList[Series[(1/2) (1/(1 - Sum[x^(2^k), {k, 0, Floor[Log[2, nmax]] + 1}]) + 1/(1 + Sum[x^(2^k), {k, 0, Floor[Log[2, nmax]] + 1}])), {x, 0, nmax}], x]

CROSSREFS

Cf. A000079, A023359, A034008, A040039, A339422, A339427.

Sequence in context: A231137 A188808 A021819 * A000021 A000022 A034805

Adjacent sequences:  A339423 A339424 A339425 * A339427 A339428 A339429

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 03 2020

STATUS

approved

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Last modified August 4 09:50 EDT 2021. Contains 346446 sequences. (Running on oeis4.)