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A097133 3*Fibonacci(n)+(-1)^n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform is A097134.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,2,1).

FORMULA

G.f. : (1+2x+2x^2)/((1+x)(1-x-x^2)); a(n)=2a(n-2)+a(n-3); a(2n)=3F(2n)+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

Cf. A000045.

Sequence in context: A067935 A228893 A272622 * A023165 A058299 A191616

Adjacent sequences:  A097130 A097131 A097132 * A097134 A097135 A097136

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 26 2004

STATUS

approved

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Last modified November 27 15:31 EST 2021. Contains 349394 sequences. (Running on oeis4.)