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

Author

Roger L. Bagula, Oct 06 2006

Keywords

• nonn

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).

Crossrefs

Cf. A051792, A000045, A028242, A030451.

Programs

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

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1 + 2*x + x^3)/(1 - x^2 - x^4))); // G. C. Greubel, 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 *)

PARI

vector(50, n, fibonacci(3/4 -(-1)^(n+1)*3/4 +(n+1)/2)) \\ G. C. Greubel, Oct 12 2018

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

Extensions

More terms from Alexander Adamchuk, Oct 08 2006