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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
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
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
KEYWORD
nonn,easy
AUTHOR
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.)