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A097133
a(n) = 3*Fibonacci(n) + (-1)^n.
4
1, 2, 4, 5, 10, 14, 25, 38, 64, 101, 166, 266, 433, 698, 1132, 1829, 2962, 4790, 7753, 12542, 20296, 32837, 53134, 85970, 139105, 225074, 364180, 589253, 953434, 1542686, 2496121, 4038806, 6534928, 10573733, 17108662, 27682394, 44791057, 72473450, 117264508
OFFSET
0,2
COMMENTS
Binomial transform is A097134.
FORMULA
G.f.: (1+2*x+2*x^2)/((1+x)*(1-x-x^2));
a(n) = 2*a(n-2)+a(n-3);
a(2*n) = 3*F(2*n)+1 = A097136(n).
MATHEMATICA
CoefficientList[Series[(1+2x+2x^2)/((1+x)(1-x-x^2)), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 2, 1}, {1, 2, 4}, 40] (* Harvey P. Dale, May 07 2011 *)
PROG
(Haskell)
a097133 n = a097133_list !! n
a097133_list = 1 : 2 : 4 : zipWith (+)
(map (* 2) $ tail a097133_list) a097133_list
-- Reinhard Zumkeller, Feb 24 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 26 2004
STATUS
approved