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A080876
a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0) = 1, a(1) = 1, and a(2) = 1.
6
1, 1, 1, 2, 4, 12, 28, 88, 208, 656, 1552, 4896, 11584, 36544, 86464, 272768, 645376, 2035968, 4817152, 15196672, 35955712, 113429504, 268377088, 846649344, 2003193856, 6319476736, 14952042496, 47169216512, 111603564544
OFFSET
0,4
FORMULA
G.f.: (-6*x^3 - 7*x^2 + 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) = (1/24 * 3^(1/2)) * (1 + sqrt(3))^n - (1/24 * 3^(1/2)) * (1 - sqrt(3))^n + (1/2 - 7/24 * 3^(1/2)) * (-(1 + sqrt(3)))^n + (1/2 + 7/24 * 3^(1/2))*(-(1 - sqrt(3)))^n. - Richard Choulet, Dec 06 2008
MATHEMATICA
CoefficientList[Series[(-6x^3-7x^2+x+1)/(4x^4-8x^2+1), {x, 0, 40}], x] (* Harvey P. Dale, Mar 04 2011 *)
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 22 2003
STATUS
approved