A130707 a(n+3) = 3*(a(n+2) - a(n+1)) + 2*a(n).
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
Offset: 0
Keywords
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).
Programs
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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
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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 *)
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)
Extensions
More terms from Emeric Deutsch, Jul 27 2007
Comments