A176281 Hankel transform of A176280.

1, 3, 12, 56, 280, 1440, 7488, 39104, 204544, 1070592, 5604864, 29345792, 153653248, 804532224, 4212572160, 22057287680, 115493404672, 604731211776, 3166413520896, 16579556016128, 86811681488896, 454551863820288

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (8,-16,8).

Formula

G.f.: (1-5*x+4*x^2)/(1-8*x+16*x^2-8*x^3) = (1-5*x+4*x^2)/((1-2*x)*(1-6*x+4*x^2)).

a(n) = 2^(n-1) + (3-sqrt(5))^n*((5-sqrt(5))/20) + (3+sqrt(5))^n*((5+sqrt(5))/20).

a(n) = 2^(n-1) + A082761(n)/2. - R. J. Mathar, Sep 30 2012

a(0)=1, a(1)=3, a(2)=12, a(n) = 8*a(n-1) - 16*a(n-2) + 8*a(n-3). - Harvey P. Dale, Aug 14 2013

a(n) = 2^(n-1)*(Fibonacci(2*n+1) + 1). - G. C. Greubel, Nov 24 2019

Maple

with(combinat); seq(2^(n-1)*(fibonacci(2*n+1) + 1), n=0..30); # G. C. Greubel, Nov 24 2019

Mathematica

CoefficientList[Series[(1-5x+4x^2)/((1-2x)(1-6x+4x^2)), {x, 0, 40}], x] (* or *) LinearRecurrence[{8, -16, 8}, {1, 3, 12}, 40] (* Harvey P. Dale, Aug 14 2013 *)

Prog

(PARI) vector(31, n, 2^(n-2)*(fibonacci(2*n-1) + 1)) \\ G. C. Greubel, Nov 24 2019
(Magma) [2^(n-1)*(Fibonacci(2*n+1) + 1): n in [0..30]]; G. C. Greubel, Nov 24 2019
(Sage) [2^(n-1)*(fibonacci(2*n+1) + 1) for n in (0..30)] # G. C. Greubel, Nov 24 2019
(GAP) List([0..30], n-> 2^(n-1)*(Fibonacci(2*n+1) + 1)); # G. C. Greubel, Nov 24 2019

Crossrefs

Cf. A000045.

Sequence in context: A185630 A284843 A107318 * A050147 A259800 A350482

Adjacent sequences: A176278 A176279 A176280 * A176282 A176283 A176284

Keyword

easy,nonn

Author

Paul Barry, Apr 14 2010

Status

approved