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 A272912 Difference sequence of the sequence A116470 of all distinct Fibonacci numbers and Lucas numbers (A000032). 2
 1, 1, 1, 1, 2, 1, 3, 2, 5, 3, 8, 5, 13, 8, 21, 13, 34, 21, 55, 34, 89, 55, 144, 89, 233, 144, 377, 233, 610, 377, 987, 610, 1597, 987, 2584, 1597, 4181, 2584, 6765, 4181, 10946, 6765, 17711, 10946, 28657, 17711, 46368, 28657, 75025, 46368, 121393, 75025 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Every term is a Fibonacci number (A000045). LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (0,1,0,1). FORMULA From Colin Barker, May 10 2016: (Start) a(n) = a(n-2)+a(n-4) for n>4. G.f.: x*(1+x-x^5) / (1-x^2-x^4). (End) a(n) = A053602(n-2), n>2. - R. J. Mathar, May 20 2016 a(n) = A123231(n-3), n>3. - Georg Fischer, Oct 23 2018 EXAMPLE A116470 = (1, 2, 3, 4, 5, 7, 8, 11, 13, 18, 21, 29, 34, 47, 55, 76,...), so that (a(n)) = (1,1,1,1,2,1,3,2,5,3,8,5,13,8,12,...). MATHEMATICA u = Table[Fibonacci[n], {n, 1, 200}]; v = Table[LucasL[n], {n, 1, 200}]; Take[Differences[Union[u, v]], 100] PROG (PARI) Vec(x*(1+x-x^5)/(1-x^2-x^4) + O(x^50)) \\ Colin Barker, May 10 2016 CROSSREFS Cf. A000045, A000032, A116470, A053602, A123231. Sequence in context: A239881 A051792 A053602 * A123231 A246995 A238782 Adjacent sequences: A272909 A272910 A272911 * A272913 A272914 A272915 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 10 2016 STATUS approved

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Last modified August 4 16:45 EDT 2024. Contains 374923 sequences. (Running on oeis4.)