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)
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
KEYWORD
nonn
AUTHOR
Paul Curtz, Jul 01 2007
EXTENSIONS
More terms from Emeric Deutsch, Jul 27 2007
STATUS
approved