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 A002536 a(n) = 8*a(n-2) - 9*a(n-4). (Formerly M3783 N1540) 2
 0, 1, 1, 5, 8, 31, 55, 203, 368, 1345, 2449, 8933, 16280, 59359, 108199, 394475, 719072, 2621569, 4778785, 17422277, 31758632, 115784095, 211059991, 769472267, 1402652240, 5113721281, 9321678001, 33984519845, 61949553848, 225852667231 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). A. Tarn, Approximations to certain square roots and the series of numbers connected therewith, Mathematical Questions and Solutions from the Educational Times, 1 (1916), 8-12. LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 Albert Tarn, Approximations to certain square roots and the series of numbers connected therewith. [Annotated scanned copy] Index entries for linear recurrences with constant coefficients, signature (0,8,0,-9). FORMULA G.f.: x(1+x-3x^2)/(1-8x^2+9x^4). A002537(n)/a(n) converges to sqrt(7). - Mario Catalani (mario.catalani(AT)unito.it), Apr 24 2003 MAPLE A002536:=-z*(-1-z+3*z**2)/(1-8*z**2+9*z**4); [Conjectured by Simon Plouffe in his 1992 dissertation.] MATHEMATICA LinearRecurrence[{0, 8, 0, -9}, {0, 1, 1, 5}, 30] (* Harvey P. Dale, May 28 2012 *) CROSSREFS Sequence in context: A361578 A049373 A304647 * A068981 A099631 A199396 Adjacent sequences: A002533 A002534 A002535 * A002537 A002538 A002539 KEYWORD nonn,easy AUTHOR N. J. A. Sloane EXTENSIONS Better description and more terms from David W. Wilson, Aug 15 1996 STATUS approved

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Last modified May 18 00:34 EDT 2024. Contains 372608 sequences. (Running on oeis4.)