A156096 Inverse binomial transform of A030186.

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

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