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A127968 a(n) = F(n+1) + (1-(-1)^n)/2, where F() = Fibonacci numbers A000045. 2
1, 2, 2, 4, 5, 9, 13, 22, 34, 56, 89, 145, 233, 378, 610, 988, 1597, 2585, 4181, 6766, 10946, 17712, 28657, 46369, 75025, 121394, 196418, 317812, 514229, 832041, 1346269, 2178310, 3524578, 5702888, 9227465, 14930353, 24157817, 39088170, 63245986, 102334156 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums of A127967.

The sequence beginning 1,1,2,2,4,... with g.f. x/(1-x-x^2) + 1/(1-x^2) has general term a(n) = F(n) + (1+(-1)^n)/2.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f.: 1 / (1 - x - x^2) + x / (1 - x^2).

G.f.: (1 + x - 2*x^2 - x^3) / ((1 - x)*(1 + x)*(1 - x - x^2)).

From Colin Barker, Jul 12 2017: (Start)

a(n) = (5 - 5*(-1)^n + 2^(-n)*sqrt(5)*(-(1-sqrt(5))^(1+n) + (1+sqrt(5))^(1+n))) / 10.

a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) for n>3.

(End)

MATHEMATICA

LinearRecurrence[{1, 2, -1, -1}, {1, 2, 2, 4}, 40] (* Harvey P. Dale, Jun 19 2013 *)

PROG

(PARI) Vec((1+x-2*x^2-x^3)/((1-x)*(1+x)*(1-x-x^2)) + O(x^50)) \\ Colin Barker, Jul 12 2017

(MAGMA) I:=[1, 2, 2, 4]; [n le 4 select I[n] else Self(n-1) +2*Self(n-2) - Self(n-3) -Self(n-4): n in [1..30]]; // G. C. Greubel, May 04 2018

CROSSREFS

Sequence in context: A191786 A007147 A230380 * A188541 A037026 A116651

Adjacent sequences:  A127965 A127966 A127967 * A127969 A127970 A127971

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Feb 09 2007

STATUS

approved

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Last modified September 16 06:38 EDT 2019. Contains 327090 sequences. (Running on oeis4.)