A117647 a(2n) = A014445(n), a(2n+1) = A015448(n+1).

0, 1, 2, 5, 8, 21, 34, 89, 144, 377, 610, 1597, 2584, 6765, 10946, 28657, 46368, 121393, 196418, 514229, 832040, 2178309, 3524578, 9227465, 14930352, 39088169, 63245986, 165580141, 267914296, 701408733

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,4,0,1).

Formula

a(n) = A059973(n+2) - A059973(n+1).

G.f.: x*(x+1)^2/(1 -4*x^2 -x^4).

a(n) = Fibonacci((6*n + 1 - (-1)^n)/4) = Fibonacci(A007494(n)). - G. C. Greubel, Jul 12 2021

Mathematica

Table[Fibonacci[(6*n+1 -(-1)^n)/4], {n, 0, 40}] (* G. C. Greubel, Jul 12 2021 *)

Prog

(Magma) I:=[0, 1, 2, 5]; [n le 4 select I[n] else 4*Self(n-2) +Self(n-4): n in [1..41]]; // G. C. Greubel, Jul 12 2021
(Sage) [fibonacci((6*n+1-(-1)^n)/4) for n in [0..40]] # G. C. Greubel, Jul 12 2021

Crossrefs

Cf. A000045, A007494, A014445, A015448, A033887, A059973.

Sequence in context: A200276 A168081 A340399 * A121568 A276464 A001005

Adjacent sequences: A117644 A117645 A117646 * A117648 A117649 A117650

Keyword

easy,nonn

Author

Creighton Dement, Apr 10 2006

Status

approved