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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.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 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: A228472 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 July 16 04:26 EDT 2019. Contains 325064 sequences. (Running on oeis4.)