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 A302126 Interleaved Fibonacci and Lucas numbers. 2
 0, 2, 1, 1, 1, 3, 2, 4, 3, 7, 5, 11, 8, 18, 13, 29, 21, 47, 34, 76, 55, 123, 89, 199, 144, 322, 233, 521, 377, 843, 610, 1364, 987, 2207, 1597, 3571, 2584, 5778, 4181, 9349, 6765, 15127, 10946, 24476, 17711, 39603, 28657, 64079, 46368, 103682, 75025, 167761 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 T. Crilly, Interleaving Integer Sequences, The Mathematical Gazette, Vol. 91, No. 520 (Mar., 2007), pp. 27-33. Wikipedia, Interleave sequence Index entries for linear recurrences with constant coefficients, signature (0,1,0,1). FORMULA a(0) = 0; a(1) = 2; a(2) = 1; a(3) = 1; a(n) = a(n-2) + a(n-4), n >= 4. G.f.: x*(2 - x)*(1 + x) / (1 - x^2 - x^4). - Colin Barker, Apr 02 2018 a(0) = 0; a(1) = 2; a(2n) = (a(2n-1) + a(2n-2))/2; a(2n+1) = a(2n) + 2*a(2n-2), n >= 1. - Daniel Forgues, Jul 29 2018 EXAMPLE a(10) = Fibonacci(5) = 5; a(11) = Lucas(5) = 11. MAPLE a:= n-> (<<0|1>, <1|1>>^iquo(n, 2, 'r'). <<2*r, 1>>)[1, 1]: seq(a(n), n=0..60); # Alois P. Heinz, Apr 23 2018 MATHEMATICA Table[{Fibonacci[n], LucasL[n]}, {n, 0, 25}] // Flatten LinearRecurrence[{0, 1, 0, 1}, {0, 2, 1, 1}, 52] Flatten@ Array[{LucasL@#, Fibonacci@#} &, 26, 0] (* or *) CoefficientList[Series[(x^3 - x^2 - 2x)/(x^4 + x^2 - 1), {x, 0, 51}], x] (* Robert G. Wilson v, Apr 02 2018 *) PROG (PARI) concat(0, Vec(x*(2 - x)*(1 + x) / (1 - x^2 - x^4) + O(x^60))) \\ Colin Barker, Apr 02 2018 (GAP) Flat(List([1..25], n->[Fibonacci(n), Lucas(1, -1, n)[2]])); # Muniru A Asiru, Apr 02 2018 CROSSREFS Interleaves A000045 and A000032. Sequence in context: A363095 A057774 A089355 * A136043 A336420 A254055 Adjacent sequences: A302123 A302124 A302125 * A302127 A302128 A302129 KEYWORD nonn,easy AUTHOR Patrick D McLean, Apr 01 2018 EXTENSIONS More terms from Colin Barker, Apr 02 2018 STATUS approved

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Last modified July 25 03:25 EDT 2024. Contains 374586 sequences. (Running on oeis4.)