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A080879
a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=1, a(2)=6.
8
1, 1, 6, 7, 44, 52, 328, 388, 2448, 2896, 18272, 21616, 136384, 161344, 1017984, 1204288, 7598336, 8988928, 56714752, 67094272, 423324672, 500798464, 3159738368, 3738010624, 23584608256, 27900891136, 176037912576, 208255086592, 1313964867584, 1554437128192
OFFSET
0,3
FORMULA
a(2n) = A080876(2n+3)/2, a(2n+1) = A080876(2n+4)/4.
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