A127968 a(n) = F(n+1) + (1-(-1)^n)/2, where F() = Fibonacci numbers A000045.

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

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 * A330627 A188541 A037026

Adjacent sequences: A127965 A127966 A127967 * A127969 A127970 A127971

Keyword

easy,nonn

Author

Paul Barry, Feb 09 2007

Status

approved