OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 8, 0, -4).
FORMULA
G.f.: (-2*x^3 - x^2 + 3*x + 1)/(4*x^4 - 8*x^2 + 1).
a(n + 4) = 8*a(n + 2) - 4*a(n). - Richard Choulet, Dec 06 2008
a(n) = (7/24*3^(1/2) + 1/2)*((1 + sqrt(3)))^n + ( - 7/24*3^(1/2) + 1/2)*((1 - sqrt(3)))^n + ( - 1/24*3^(1/2))*( - (1 + sqrt(3)))^n + (1/24*3^(1/2))*( - ((1 - sqrt(3))))^n. - Richard Choulet, Dec 06 2008
MAPLE
a:= n-> (Matrix([[22, 7, 3, 1]]). Matrix(4, (i, j)-> if (i=j-1) then 1 elif j=1 then [0, 8, 0, -4][i] else 0 fi)^(n))[1, 4]: seq(a(n), n=0..26); # Alois P. Heinz, Aug 23 2008
MATHEMATICA
a[0]=1; a[1]=3; a[2]=7; a[3]=22; a[n_] := a[n] = 8*a[n-2] - 4*a[n-4]; Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Jun 15 2015, after Richard Choulet *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 22 2003
STATUS
approved