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A135532 a(n) = 2*a(n-1) + a(n-2), with a(0)= -1, a(1)= 3. 10
-1, 3, 5, 13, 31, 75, 181, 437, 1055, 2547, 6149, 14845, 35839, 86523, 208885, 504293, 1217471, 2939235, 7095941, 17131117, 41358175, 99847467, 241053109, 581953685, 1404960479, 3391874643, 8188709765, 19769294173, 47727298111, 115223890395, 278175078901, 671574048197 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Double binomial transform of [1, 3, -5, 13, -31, 75, -181,...] = the Pell-like sequence A048655: (1, 5, 11, 27, 65, 157,...). - Gary W. Adamson, Jul 23 2008

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (2,1).

FORMULA

From R. J. Mathar, Feb 23 2008: (Start)

O.g.f.: (1 - 5*x)/(x^2 + 2x - 1).

a(n) = 5*A000129(n) - A000129(n+1). (End)

a(n) = (1/2)*( (2*sqrt(2) - 1)*(1 + sqrt(2))^n - (1 + 2*sqrt(2))*(1 - sqrt(2))^n ), with n>=0. - Paolo P. Lava, Jun 09 2008

a(n) = ((3+sqrt(2))*(1+sqrt(2))^n + (3-sqrt(2))*(1-sqrt(2))^n)/2 with offset 0. - Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009

MATHEMATICA

a=1; b=3; c=1; lst={-1, b}; Do[c=a+b+c; AppendTo[lst, c]; a=b; b=c, {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 23 2009 *)

LinearRecurrence[{2, 1}, {-1, 3}, 25] (* G. C. Greubel, Oct 17 2016 *)

PROG

(PARI) a(n)=([0, 1; 1, 2]^n*[-1; 3])[1, 1] \\ Charles R Greathouse IV, Oct 17 2016

CROSSREFS

Cf. A048655.

Sequence in context: A190667 A062304 A281874 * A127600 A262237 A051401

Adjacent sequences:  A135529 A135530 A135531 * A135533 A135534 A135535

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Feb 21 2008

EXTENSIONS

More terms from R. J. Mathar, Feb 23 2008

STATUS

approved

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Last modified November 15 11:13 EST 2019. Contains 329144 sequences. (Running on oeis4.)