A137447 a(n) = 4*a(n-4) for n>3, a(0)=-1, a(1)=-4, a(2)=2, a(3)=12.

-1, -4, 2, 12, -4, -16, 8, 48, -16, -64, 32, 192, -64, -256, 128, 768, -256, -1024, 512, 3072, -1024, -4096, 2048, 12288, -4096, -16384, 8192, 49152, -16384, -65536, 32768, 196608, -65536, -262144, 131072, 786432, -262144, -1048576, 524288, 3145728, -1048576

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 (0,0,0,4).

Formula

G.f.: (1+4*x-2*x^2-12*x^3)/(4*x^4-1). - Harvey P. Dale, Jun 27 2011

From Bruno Berselli, Nov 02 2011: (Start)

a(n) = (1-(-1)^n-2*(3-2*(-1)^n)*(-1)^floor(n/2))*2^(floor(n/2)-1).

a(2n) = -A122803(n).

a(2n+1) = (-1)^(n+1)*A084221(n+2). (End)

E.g.f.: (1/sqrt(2))*( sinh(sqrt(2)*x) - 5*sin(sqrt(2)*x) - sqrt(2)*cos(sqrt(2)*x) ). - G. C. Greubel, Sep 15 2023

Mathematica

LinearRecurrence[{0, 0, 0, 4}, {-1, -4, 2, 12}, 50] (* or *) CoefficientList[ Series[(1+4x-2x^2-12x^3)/(4x^4-1), {x, 0, 50}], x] (* Harvey P. Dale, Jun 27 2011 *)

Prog

(Magma) &cat[[-(-2)^n, 2^n-5*(-2)^n]: n in [0..20]];  // Bruno Berselli, Nov 02 2011
(SageMath)
def A137447(n): return 2^(n//2)*(-1)^(n//2+1) if n%2==0 else 2^((n-1)//2)*(1 - 5*(-1)^((n-1)//2))
[A137447(n) for n in range(51)] # G. C. Greubel, Sep 15 2023

Crossrefs

Cf. A084221, A102561, A122803.

Sequence in context: A188134 A226725 A354190 * A353749 A077015 A077016

Adjacent sequences: A137444 A137445 A137446 * A137448 A137449 A137450

Keyword

sign,easy

Author

Paul Curtz, Apr 18 2008

Extensions

More terms from Harvey P. Dale, Jun 27 2011

Status

approved