OFFSET
0,3
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,8,0,-4).
FORMULA
G.f.: (-x^3 - 2*x^2 + x + 1)/(4*x^4 - 8*x^2 + 1).
a(n) = ((9/16)*sqrt(3) - 7/16)*(1 + sqrt(3))^n + (-(9/16)*sqrt(3) - 7/16)*(1 - sqrt(3))^n + (-(19/48)*sqrt(3) + 15/16)*(-(1 + sqrt(3)))^n + ((19/48)*sqrt(3) + 15/16)*(-(1 - sqrt(3)))^n. - Richard Choulet, Dec 06 2008
a(n+4) = 8*a(n+2) - 4*a(n). - Richard Choulet, Dec 06 2008
MAPLE
a:= n-> (<<0|1>, <-4|8>>^floor(n/2). <<1, 6+(n mod 2)>>)[1, 1]:
seq(a(n), n=0..30); # Alois P. Heinz, Mar 18 2023
MATHEMATICA
LinearRecurrence[{0, 8, 0, -4}, {1, 1, 6, 7}, 30] (* Harvey P. Dale, Mar 10 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 22 2003
STATUS
approved