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, 1134903170, 2971215073, 4807526976, 12586269025, 20365011074, 53316291173

Offset: 0

Author

Creighton Dement, Apr 10 2006

Keywords

• easy
• nonn

Comments

Because of g.f. in Formula section, numbers k + 1 such that A088207(k)/k is an integer. - Ctibor O. Zizka, Apr 07 2025

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).

Crossrefs

Cf. A000045, A001950, A007494, A014445, A015448, A033887, A059973, A088207.

Programs

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

Mathematica

Table[Fibonacci[(6*n+1 -(-1)^n)/4], {n, 0, 40}] (* 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

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