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 A049686 a(n) = Fibonacci(8n)/3. 3
 0, 7, 329, 15456, 726103, 34111385, 1602508992, 75283811239, 3536736619241, 166151337293088, 7805576116155895, 366695926122033977, 17226902951619441024, 809297742799991694151, 38019767008647990184073, 1786119751663655546957280, 83909608561183162716808087, 3941965482623944992143022809 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) = (t(i+4n) - t(i))/(t(i+2n+1) - t(i+2n-1)), where (t) is any sequence of the form t(n+2) = 8t(n+1) - 8t(n) + t(n-1) or of the form t(n+1) = 7t(n) - t(n-1) without regard to initial values as long as t(i+2n+1) - t(i+2n-1) != 0. - Klaus Purath, Jun 23 2024 LINKS Indranil Ghosh, Table of n, a(n) for n = 0..597 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (47,-1). FORMULA a(n) = 47*a(n-1) - a(n-2), n>1. a(0)=0, a(1)=7. G.f.: 7*x/(1-47*x+x^2). a(n) = A004187(2n). a(n) = 7*A049668(n). - R. J. Mathar, Oct 26 2015 E.g.f.: 2*exp(47*x/2)*sinh(21*sqrt(5)*x/2)/(3*sqrt(5)). - Stefano Spezia, Dec 14 2019 EXAMPLE a(2) = F(8 * 2) / 3 = F(16) / 3 = 987 / 3 = 329. - Indranil Ghosh, Feb 05 2017 MAPLE with(combinat); seq( fibonacci(8*n)/3, n=0..20); # G. C. Greubel, Dec 14 2019 MATHEMATICA Fibonacci[8(Range[20]-1)]/3 (* G. C. Greubel, Dec 14 2019 *) LinearRecurrence[{47, -1}, {0, 7}, 20] (* Harvey P. Dale, Dec 27 2019 *) PROG (PARI) a(n) = fibonacci(8*n)/3; \\ Michel Marcus, Feb 05 2017 (Magma) [Fibonacci(8*n)/3: n in [0..20]]; // G. C. Greubel, Dec 14 2019 (Sage) [fibonacci(8*n)/3 for n in (0..20)] # G. C. Greubel, Dec 14 2019 (GAP) List([0..20], n-> Fibonacci(8*n)/3 ); # G. C. Greubel, Dec 14 2019 CROSSREFS Cf. A000045, A004187, A049668. Sequence in context: A002000 A374418 A092588 * A177019 A160432 A324233 Adjacent sequences: A049683 A049684 A049685 * A049687 A049688 A049689 KEYWORD nonn,easy AUTHOR Clark Kimberling EXTENSIONS Better description and more terms from Michael Somos STATUS approved

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Last modified August 10 05:56 EDT 2024. Contains 375044 sequences. (Running on oeis4.)