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A211164 Number of compositions of n with at most one odd part. 2
1, 1, 1, 3, 2, 8, 4, 20, 8, 48, 16, 112, 32, 256, 64, 576, 128, 1280, 256, 2816, 512, 6144, 1024, 13312, 2048, 28672, 4096, 61440, 8192, 131072, 16384, 278528, 32768, 589824, 65536, 1245184, 131072, 2621440, 262144, 5505024, 524288, 11534336, 1048576, 24117248 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-4)

FORMULA

G.f.: -(2*x^4-x^3-3*x^2+x+1)/(-4*x^4+4*x^2-1).

From Colin Barker, May 07 2016: (Start)

a(n) = 2^((n-7)/2+5/2) for n>0 and even.

a(n) = 2^((n-7)/2)*(2*n+6) for n>0 and odd.

a(n) = 4*a(n-2)-4*a(n-4) for n>4.

(End)

EXAMPLE

a(3) = 3: [3], [1,2], [2,1].

a(4) = 2: [4], [2,2].

a(5) = 8: [5], [3,2], [2,3], [1,4], [4,1], [1,2,2], [2,1,2], [2,2,1].

a(6) = 4: [6], [4,2], [2,4], [2,2,2].

a(8) = 8: [8], [4,4], [2,6], [6,2], [2,2,4], [4,2,2], [2,4,2], [2,2,2,2].

MAPLE

a:= n-> `if`(n<2, 1, 2^iquo(n-2, 2) *

        `if`(irem(n, 2)=0, 1, iquo(n+3, 2))):

seq(a(n), n=0..60);

PROG

(PARI) Vec((1-x)^2*(1+x)*(1+2*x)/(1-2*x^2)^2 + O(x^50)) \\ Colin Barker, May 07 2016

CROSSREFS

Bisection gives: A011782 (even part), A001792 (odd part).

Cf. A208354.

Sequence in context: A162728 A127300 A129199 * A097018 A127541 A053219

Adjacent sequences:  A211161 A211162 A211163 * A211165 A211166 A211167

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Jan 30 2013

STATUS

approved

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Last modified July 19 09:33 EDT 2019. Contains 325155 sequences. (Running on oeis4.)