A226649 Fibonacci shuffles: a(2n) = A000071(n) and a(2n+1) = A001611(n+2).

0, 2, 0, 3, 1, 4, 2, 6, 4, 9, 7, 14, 12, 22, 20, 35, 33, 56, 54, 90, 88, 145, 143, 234, 232, 378, 376, 611, 609, 988, 986, 1598, 1596, 2585, 2583, 4182, 4180, 6766, 6764, 10947, 10945, 17712, 17710, 28658, 28656, 46369, 46367, 75026, 75024, 121394, 121392, 196419, 196417, 317812, 317810

Offset: 0

Author

V. T. Jayabalaji, Jun 14 2013

Keywords

• nonn
• easy

Comments

a(2*n+1) = a(2*n) + A157725(n); a(2*n) = a(2*n-1) - 2 for n > 0. - Reinhard Zumkeller, Jul 30 2013

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (-1,1,1,1,1).

Crossrefs

Cf. A000071, A001611, A096748.

Programs

Haskell

import Data.List (transpose)
a226649 n = a226649_list !! n
a226649_list = concat $ transpose [a000071_list, drop 2 a001611_list]
-- Reinhard Zumkeller, Jul 30 2013

Mathematica

LinearRecurrence[{-1,1,1,1,1},{0,2,0,3,1},60] (* Harvey P. Dale, Sep 12 2018 *)

Formula

G.f. -x*(2+x^2+2*x^3+2*x) / ( (1+x)*(x^4+x^2-1) ). - R. J. Mathar, Jul 15 2013

a(n) + a(n+1) = A096748(n+2). - R. J. Mathar, Jul 15 2013

a(2n-1) - 1 = a(2n) + 1 = fib(n+1) = A000045(n+1) for n > 0. - T. D. Noe, Jul 23 2013