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 A108362 Pair reversal of Fibonacci numbers. 2
 1, 0, 2, 1, 5, 3, 13, 8, 34, 21, 89, 55, 233, 144, 610, 377, 1597, 987, 4181, 2584, 10946, 6765, 28657, 17711, 75025, 46368, 196418, 121393, 514229, 317811, 1346269, 832040, 3524578, 2178309, 9227465, 5702887, 24157817, 14930352, 63245986, 39088169, 165580141 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Here Fibonacci numbers are swapped in pairs, beginning with the pair (F(0),F(1)) changed in (F(1),F(0)). Similar to A135992, which starts switching F(1) and F(2). - Giuseppe Coppoletta, Mar 04 2015 LINKS Table of n, a(n) for n=0..40. Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1). FORMULA G.f.: (1-x^2+x^3)/(1-3x^2+x^4). a(n) = 3*a(n-2) - a(n-4) for n>3 with a(0)=1, a(1)=0, a(2)=2, a(3)=1. a(n) = (sqrt(5)/2-1/2)^n * ((-1)^n/2-sqrt(5)/10)+(sqrt(5)/2+1/2)^n * (sqrt(5)*(-1)^n/10+1/2). From Giuseppe Coppoletta, Mar 04 2015: (Start) a(2n) = A000045(2n+1), a(2n+1) = A000045(2n). a(2n) = a(2n-1) + 2*a(2n-2), a(2n+1) = (a(2n) + a(2n-1))/2. (End) a(n) = ((-1)^n * Fibonacci(n) + Lucas(n))/2. - Vladimir Reshetnikov, Sep 24 2016 EXAMPLE a(6) = Fibonacci(7) = 13, a(7) = Fibonacci(6) = 8. MAPLE a:= n-> (<<0|1>, <1|1>>^(n+(-1)^n))[1, 2]: seq(a(n), n=0..40); # Alois P. Heinz, Sep 27 2023 MATHEMATICA Flatten[Reverse/@Partition[Fibonacci[Range[0, 40]], 2]] (* or *) LinearRecurrence[{0, 3, 0, -1}, {1, 0, 2, 1}, 40] (* Harvey P. Dale, Sep 09 2015 *) Table[((-1)^n Fibonacci[n] + LucasL[n])/2, {n, 0, 40}] (* Vladimir Reshetnikov, Sep 24 2016 *) PROG (Sage) [fibonacci(n+(-1)^n) for n in range(39)] # Giuseppe Coppoletta, Mar 04 2015 (PARI) Vec((1-x^2+x^3)/(1-3*x^2+x^4) + O(x^50)) \\ Michel Marcus, Mar 04 2015 CROSSREFS Cf. A000045, A001906, A135992. Sequence in context: A355562 A194809 A113178 * A171090 A141506 A345454 Adjacent sequences: A108359 A108360 A108361 * A108363 A108364 A108365 KEYWORD easy,nonn AUTHOR Paul Barry, May 31 2005 STATUS approved

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Last modified March 3 08:35 EST 2024. Contains 370499 sequences. (Running on oeis4.)