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A084170 a(n) = 5*2^n/3 + (-1)^n/3 - 1. 6
1, 2, 6, 12, 26, 52, 106, 212, 426, 852, 1706, 3412, 6826, 13652, 27306, 54612, 109226, 218452, 436906, 873812, 1747626, 3495252, 6990506, 13981012, 27962026, 55924052, 111848106, 223696212, 447392426, 894784852, 1789569706, 3579139412 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Original name of this sequence: Generalized Jacobsthal numbers.

LINKS

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

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

FORMULA

a(n) = 2*a(n-1) +a(n-2) -2*a(n-3), n>2.

a(n) = a(n-1)+2*a(n-2)+2, a(0)=1, a(1)=2.

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

E.g.f.: 5*exp(2*x)/3-exp(x)+exp(-x)/3.

a(n+1) = A000975(n+2)+A000975(n).

a(2*n+1)-2 = 10*A000975(n); a(2*n+2)-6 = 20*A000975(n).

a(n+2*k) - a(n) = 5*A002450(k)*2^n = A146882(k-1)*2^n, k=0,1,2,... - Paul Curtz, Jun 15 2011

a(n) = A169969(2n)-1, n>=1; a(n) = 3*2^(n-1)-1+A169969(2n-7), n>=5 . - Yosu Yurramendi, Jul 05 2016

a(n+3) = 15*2^n-2-a(n), n>=0, a(0)=1, a(1)=2, a(2)=6. - Yosu Yurramendi, Jul 05 2016

a(n) + A026644(n) = 3*2^n-2, n>=1;  a(n+3) = 3*2^(n+2) + A026644(n), n>=1 . - Yosu Yurramendi, Jul 05 2016

MATHEMATICA

LinearRecurrence[{2, 1, -2}, {1, 2, 6}, 40] (* or *) Table[5*2^n/3+(-1)^n/3-1, {n, 0, 40}] (* Harvey P. Dale, Jan 29 2012 *)

PROG

(PARI) a(n)=(5*2^n)\/3-1 \\ Charles R Greathouse IV, Jul 01 2011

(MAGMA) [5*2^n/3 + (-1)^n/3 - 1: n in [0..35]]; // Vincenzo Librandi, Jul 05 2011

CROSSREFS

Sequence in context: A300120 A246584 A054454 * A245264 A052971 A289443

Adjacent sequences:  A084167 A084168 A084169 * A084171 A084172 A084173

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 18 2003

STATUS

approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)