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A135098 First differences of A135094. 3
1, 2, 5, 10, 22, 44, 92, 184, 376, 752, 1520, 3040, 6112, 12224, 24512, 49024, 98176, 196352, 392960, 785920, 1572352, 3144704, 6290432, 12580864, 25163776, 50327552, 100659200, 201318400, 402644992, 805289984, 1610596352, 3221192704 (list; graph; refs; listen; history; text; internal format)
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 (2, 2, -4).

FORMULA

From R. J. Mathar, Feb 15 2008: (Start)

O.g.f.: (2*x+1) / (2(2x^2-1)) -3 / (2(2*x-1)).

a(n) = (-016116(n+1) +A007283(n)) / 2 . (End)

G.f.: (1 - x)*(1 + x) / ((1 - 2*x)*(1 - 2*x^2)). - Arkadiusz Wesolowski, Oct 24 2013

From G. C. Greubel, Sep 23 2016: (Start)

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

E.g.f.: (1/4)*( 3*exp(2*x) - 2*cosh(sqrt(2)*x) - sqrt(2)*sinh(sqrt(2)*x). (End)

MATHEMATICA

Table[2^((n - 5)/2)*( 3*2^((n + 1)/2) - (1 - (-1)^n) - (1 + (-1)^n)*Sqrt[2] ), {n, 1, 50}] (* or *) LinearRecurrence[{2, 2, -4}, {1, 2, 5}, 25] (* G. C. Greubel, Sep 23 2016 *)

PROG

(PARI) a(n)=([0, 1, 0; 0, 0, 1; -4, 2, 2]^n*[1; 2; 5])[1, 1] \\ Charles R Greathouse IV, Sep 23 2016

CROSSREFS

Sequence in context: A026633 A093370 A094537 * A136488 A045621 A026655

Adjacent sequences:  A135095 A135096 A135097 * A135099 A135100 A135101

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Feb 12 2008

EXTENSIONS

More terms from R. J. Mathar, Feb 15 2008

STATUS

approved

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Last modified March 30 19:49 EDT 2020. Contains 333127 sequences. (Running on oeis4.)