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A211227 Row sums of A211226. 3
1, 2, 3, 4, 8, 8, 20, 16, 48, 32, 112, 64, 256, 128, 576, 256, 1280, 512, 2816, 1024, 6144, 2048, 13312, 4096, 28672, 8192, 61440, 16384, 131072, 32768, 278528, 65536, 589824, 131072, 1245184, 262144, 2621440, 524288, 5505024 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The odd-indexed terms of the sequence a(2*n-1) count the compositions of n+1, while the even-indexed terms a(2*n) count the total number of parts in the composition of n+1. Compare with A211228.

LINKS

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

FORMULA

a(n) = sum {k = 0..n } f(n)/(f(k)*f(n-k)), where f(n) := (floor(n/2))!.

a(2*n-1) = 2^n = A000079(n); a(2*n) = (n+2)*2^(n-1) = A001792(n).

O.g.f.: (1+2*x-x^2-4*x^3)/(1-2*x^2)^2 = 1 + 2*x + 3*x^2 + 4*x^3 + 8*x^4 + ....

E.g.f.: cosh(sqrt(2)*x) + (4+x)/(2*sqrt(2))*sinh(sqrt(2)*x) = 1 + 2*x + 3*x^2/2! + 4*x^3/3! + 8*x^4/4! + .....

EXAMPLE

The four compositions of 3 are 1+1+1, 1+2, 2+1 and 3 having 8 parts in total. Hence a(3) = 4 and a(4) = 8.

CROSSREFS

Cf. A000079, A001792, A211226.

Sequence in context: A242065 A056424 A050324 * A019949 A172002 A274927

Adjacent sequences:  A211224 A211225 A211226 * A211228 A211229 A211230

KEYWORD

nonn,easy

AUTHOR

Peter Bala, Apr 05 2012

STATUS

approved

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Last modified June 24 18:38 EDT 2021. Contains 345419 sequences. (Running on oeis4.)