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A140966 a(n) = (5 + (-2)^n)/3. 14
2, 1, 3, -1, 7, -9, 23, -41, 87, -169, 343, -681, 1367, -2729, 5463, -10921, 21847, -43689, 87383, -174761, 349527, -699049, 1398103, -2796201, 5592407, -11184809, 22369623, -44739241, 89478487, -178956969, 357913943 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Inverse binomial transform of A048573.

This is an example of the case k=-1 of sequences with recurrences a(n) = k*a(n-1) + (k+3)*a(n-2) - (2*k+2)*a(n-3).

The case k=1 is covered, for example, by A097163, A135520, A136326, A136336, or A137208.

Sequences with k=2 are A094554 and A094555.

Sequences with k=3 are A084175, A108924, and A139818.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = -a(n-1) + 2*a(n-2).

G.f.: (2+3*x)/((1-x)*(1+2*x)).

a(n+1) - a(n) = (-1)^(n+1)*A000079(n).

a(n+3) = (-1)^n*A083582(n).

a(n+1) - 2*a(n) = -a(n+2).

a(n+1) - 3*a(n) = 5*(-1)^(n+1)*A078008(n) = (-1)^(n+1)*A001045(n-1).

a(2n+3) = -A083584(n), a(2n) = A163834(n). - Philippe Deléham, Feb 24 2014

MATHEMATICA

(5+(-2)^Range[0, 30])/3 (* or *) LinearRecurrence[{-1, 2}, {2, 1}, 40] (* Harvey P. Dale, Apr 23 2019 *)

PROG

(Magma) [( 5+(-2)^n)/3: n in [0..35]]; // Vincenzo Librandi, Jul 05 2011

(PARI) a(n)=(5+(-2)^n)/3 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Sequence in context: A165401 A319916 A213074 * A058036 A136179 A185176

Adjacent sequences: A140963 A140964 A140965 * A140967 A140968 A140969

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Jul 27 2008

EXTENSIONS

Definition simplified by R. J. Mathar, Sep 11 2009

STATUS

approved

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Last modified December 6 08:36 EST 2022. Contains 358605 sequences. (Running on oeis4.)