

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 period3 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*x1)/(x^2x+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[n1]a[n2])+2a[n3]}, 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



