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A156096 Inverse binomial transform of A030186. 2
1, 1, 4, 6, 18, 32, 84, 164, 400, 824, 1928, 4096, 9360, 20240, 45632, 99680, 223008, 489984, 1091392, 2405952, 5345536, 11806592, 26194048, 57917440, 128389376, 284057856, 629392384, 1393010176, 3085685248, 6830825472, 15128761344 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A030186 = (1, 2, 7, 22, 71, 228, 733, 2356, 7573, 24342, ...).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,4,2).

FORMULA

a(n) = A007318^(-1) * A030186

From R. J. Mathar, Feb 10 2009: (Start)

a(n) = 4*a(n-2) + 2*a(n-3).

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

EXAMPLE

a(3) = 6 = (-1, 3, -3, 1) dot (1, 2, 7, 22) = (-1, 6, -21, 22) = 6.

MAPLE

seq(coeff(series((1+x)/(1-4*x^2-2*x^3), x, n+1), x, n), n = 0..40); # G. C. Greubel, Oct 27 2019

MATHEMATICA

LinearRecurrence[{0, 4, 2}, {1, 1, 4}, 40] (* Harvey P. Dale, Apr 05 2014 *)

PROG

(PARI) my(x='x+O('x^40)); Vec((1+x)/(1-4*x^2-2*x^3)) \\ G. C. Greubel, Oct 27 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)/(1-4*x^2-2*x^3) )); // G. C. Greubel, Oct 27 2019

(Sage)

def A156096_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P((1+x)/(1-4*x^2-2*x^3)).list()

A156096_list(40) # G. C. Greubel, Oct 27 2019

(GAP) a:=[1, 1, 4];; for n in [4..40] do a[n]:=4*a[n-2]+2*a[n-3]; od; a; # G. C. Greubel, Oct 27 2019

CROSSREFS

Cf. A030186.

Sequence in context: A287682 A209236 A182643 * A281861 A218898 A088810

Adjacent sequences:  A156093 A156094 A156095 * A156097 A156098 A156099

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Feb 03 2009

EXTENSIONS

More terms from R. J. Mathar, Feb 10 2009

STATUS

approved

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Last modified May 9 07:36 EDT 2021. Contains 343692 sequences. (Running on oeis4.)