A136258 a(n) = 2*a(n-1) - 2*a(n-2), with a(0)=1, a(1)=5.

1, 5, 8, 6, -4, -20, -32, -24, 16, 80, 128, 96, -64, -320, -512, -384, 256, 1280, 2048, 1536, -1024, -5120, -8192, -6144, 4096, 20480, 32768, 24576, -16384, -81920, -131072, -98304, 65536, 327680, 524288, 393216, -262144, -1310720, -2097152, -1572864, 1048576

Offset

0,2

Comments

Sequence opposite in sign to its second differences.

Binomial transform of 1, 4, -1, -4.

A bisection gives A135520.

This sequence with offset 0 is the binomial transform of (-1)^floor(n/2)*A010685(n). - R. J. Mathar, Feb 22 2009

Links

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

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

Formula

a(4n+1) = 5*(-4)^n, a(4n+3) = 6*(-4)^n. - M. F. Hasler, May 01 2008

G.f.: x*(1+3*x)/(1-2*x+2*x^2). - R. J. Mathar, Feb 22 2009

From Paul Curtz, Apr 27 2011: (Start)

a(n)= -4 * a(n-4).

a(n)= 3*A009545(n) + A009545(n+1). (End)

E.g.f.: exp(x)*( cos(x) + 4*sin(x) ). - G. C. Greubel, Dec 02 2021

Mathematica

LinearRecurrence[{2, -2}, {1, 5}, 50] (* Harvey P. Dale, May 21 2014 *)

Prog

(PARI) vector(100, n, t=if(n<3, [t1=1, 5][n], -2*t1+2*t1=t)) \\ M. F. Hasler, May 01 2008
(Magma) [n le 2 select 5^(n-1) else 2*(Self(n-1) - Self(n-2)): n in [1..41]]; // G. C. Greubel, Dec 02 2021
(Sage)
A136258=BinaryRecurrenceSequence(2, -2, 1, 5)
[A136258(n) for n in (0..40)] # G. C. Greubel, Dec 02 2021

Crossrefs

Cf. A010685, A135520.

Sequence in context: A296486 A011424 A011495 * A102519 A334849 A199265

Adjacent sequences: A136255 A136256 A136257 * A136259 A136260 A136261

Keyword

sign,easy

Author

Paul Curtz, Mar 18 2008

Extensions

Edited and extended by M. F. Hasler, May 01 2008

Offset corrected Paul Curtz, Apr 27 2011

Status

approved