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

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

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 *)

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

Extensions

Better description and more terms from David W. Wilson, Aug 15 1996