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%I #22 Oct 06 2017 21:38:18
%S 1,2,1,5,2,13,5,34,13,89,34,233,89,610,233,1597,610,4181,1597,10946,
%T 4181,28657,10946,75025,28657,196418,75025,514229,196418,1346269,
%U 514229,3524578,1346269,9227465,3524578,24157817,9227465,63245986,24157817
%N a(n) = Fibonacci(n+1) - (-1)^n*Fibonacci(n).
%C Binomial transform is Fibonacci(n) + Fibonacci(2n+1) = A087124(n).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-1).
%F a(2n) = Fibonacci(2n-1), a(2n+1) = Fibonacci(2n+3).
%F G.f.: (1-x)*(1+3*x+x^2)/((1+x-x^2)*(1-x-x^2)). - _Colin Barker_, Apr 16 2012
%F a(n) = 3*a(n-2) - a(n-4) for n > 3. - _Wesley Ivan Hurt_, Oct 05 2017
%p with(combinat): A087123:=n->fibonacci(n+1)-(-1)^n*fibonacci(n): seq(A087123(n), n=0..50); # _Wesley Ivan Hurt_, Oct 05 2017
%t MapIndexed[#2 - (-1)^#1*#3 & @@ {First@ #2 - 1, Last@ #1, First@ #1} &, Partition[Fibonacci@ Range[0, 36], 2, 1]] (* or *)
%t CoefficientList[Series[(1 - x) (1 + 3 x + x^2)/((1 + x - x^2) (1 - x - x^2)), {x, 0, 38}], x] (* _Michael De Vlieger_, Oct 06 2017 *)
%o (PARI) a(n) = fibonacci(n+1)-(-1)^n*fibonacci(n); \\ _Altug Alkan_, Oct 06 2017
%Y Cf. A000045, A001519, A001906, A087124.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Aug 15 2003
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