A002536 a(n) = 8*a(n-2) - 9*a(n-4). (Formerly M3783 N1540)

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

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