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

Author

Gary W. Adamson, Feb 03 2009

Keywords

• nonn

Comments

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

Examples

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

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).

Crossrefs

Cf. A030186.

Programs

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

Magma

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

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 *)

PARI

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

Sage

def A156096_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+x)/(1-4*x^2-2*x^3)).list()
A156096_list(40) # G. C. Greubel, Oct 27 2019

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)

Extensions

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