A123231 Row sums of A123230.

1, 2, 1, 3, 2, 5, 3, 8, 5, 13, 8, 21, 13, 34, 21, 55, 34, 89, 55, 144, 89, 233, 144, 377, 233, 610, 377, 987, 610, 1597, 987, 2584, 1597, 4181, 2584, 6765, 4181, 10946, 6765, 17711, 10946, 28657, 17711, 46368, 28657, 75025, 46368, 121393, 75025, 196418

Offset

1,2

Comments

All terms are Fibonacci numbers A000045: a(2n-1) = Fibonacci(n), a(2n) = Fibonacci(n+2), a(2n-1) = a(2n+2). - Alexander Adamchuk, Oct 08 2006

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

From Alexander Adamchuk, Oct 08 2006: (Start)

a(n) = Fibonacci(A028242(n+2)).

a(n) = Fibonacci(A030451(n+1)).

a(n) = Fibonacci(3/4 -(-1)^(n+1)*3/4 +(n+1)/2). (End)

a(n) = A053602(n+1) = A097594(n-5). - R. J. Mathar, Mar 08 2011

G.f. -x*(1+2*x+x^3) / ( -1+x^2+x^4 ). - R. J. Mathar, Mar 08 2011

a(n) = a(n-2) + a(n-4). - Muniru A Asiru, Oct 12 2018

Maple

seq(coeff(series(-x*(1+2*x+x^3)/(x^4+x^2-1), x, n+1), x, n), n = 1 .. 50); # Muniru A Asiru, Oct 12 2018

Mathematica

p[0, x] = 1; p[1, x] = x + 1; p[k_, x_] := p[k, x] = x*p[k - 1, x] + (-1)^(n + 1)p[k - 2, x]; Table[Sum[CoefficientList[p[n, x], x][[m]], {m, 1, n + 1}], {n, 0, 20}]
Rest[Flatten[Reverse/@Partition[Fibonacci[Range[30]], 2, 1]]] (* Harvey P. Dale, Mar 19 2013 *)

Prog

(PARI) vector(50, n, fibonacci(3/4 -(-1)^(n+1)*3/4 +(n+1)/2)) \\ G. C. Greubel, Oct 12 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1 + 2*x + x^3)/(1 - x^2 - x^4))); // G. C. Greubel, Oct 12 2018
(GAP) a:=[1, 2, 1, 3];; for n in [5..50] do a[n]:=a[n-2]+a[n-4]; od; a; # Muniru A Asiru, Oct 12 2018

Crossrefs

Cf. A051792, A000045, A028242, A030451.

Sequence in context: A051792 A053602 A272912 * A246995 A238782 A378749

Adjacent sequences: A123228 A123229 A123230 * A123232 A123233 A123234

Keyword

nonn

Author

Roger L. Bagula, Oct 06 2006

Extensions

More terms from Alexander Adamchuk, Oct 08 2006

Status

approved