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A130707 a(n+3) = 3*(a(n+2) - a(n+1)) + 2*a(n). 3
1, 2, 2, 2, 4, 10, 22, 44, 86, 170, 340, 682, 1366, 2732, 5462, 10922, 21844, 43690, 87382, 174764, 349526, 699050, 1398100, 2796202, 5592406, 11184812, 22369622, 44739242, 89478484, 178956970, 357913942, 715827884, 1431655766, 2863311530 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of period-3 sequence with period 1 1 -1.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3, -3, 2).

FORMULA

a(n) = 2^n/3 + 4*(-1)^n*(1/3)*cos((2n+1)*Pi/3). - Emeric Deutsch, Jul 27 2007

From R. J. Mathar, Nov 18 2007: (Start)

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

a(n) = (2*A057079(n) + 2^n)/3. (End)

a(n) = (1/3)*(1/2 - (1/2)*i*sqrt(3))^n + (1/3)*(1/2 + (1/2)*i*sqrt(3))^n + (1/3)*2^n + (1/3)*i*(1/2 - (1/2)*i*sqrt(3))^n*sqrt(3) - (1/3)*i*(1/2 + (1/2)*i*sqrt(3))^n*sqrt(3), with n >= 0. - Paolo P. Lava, May 10 2010

MAPLE

a:=proc(n) options operator, arrow: (1/3)*2^n+(4/3)*(-1)^n*cos((1/3)*(2*n+1)*Pi) end proc: seq(a(n), n = 0 .. 33); # Emeric Deutsch, Jul 27 2007

MATHEMATICA

RecurrenceTable[{a[0]==1, a[1]==a[2]==2, a[n]==3(a[n-1]-a[n-2])+2a[n-3]}, a, {n, 40}] (* or *) LinearRecurrence[{3, -3, 2}, {1, 2, 2}, 40] (* Harvey P. Dale, Jan 18 2015 *)

CROSSREFS

Sequence in context: A231382 A213270 A307522 * A131562 A260786 A107902

Adjacent sequences:  A130704 A130705 A130706 * A130708 A130709 A130710

KEYWORD

nonn

AUTHOR

Paul Curtz, Jul 01 2007

EXTENSIONS

More terms from Emeric Deutsch, Jul 27 2007

STATUS

approved

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Last modified August 14 01:55 EDT 2020. Contains 336476 sequences. (Running on oeis4.)