%I M3783 N1540 #48 Oct 17 2023 05:44:17

%S 0,1,1,5,8,31,55,203,368,1345,2449,8933,16280,59359,108199,394475,

%T 719072,2621569,4778785,17422277,31758632,115784095,211059991,

%U 769472267,1402652240,5113721281,9321678001,33984519845,61949553848,225852667231

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

%D Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D 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.

%H Harvey P. Dale, <a href="/A002536/b002536.txt">Table of n, a(n) for n = 0..1000</a>

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%H Albert Tarn, <a href="/A001333/a001333_1.pdf">Approximations to certain square roots and the series of numbers connected therewith</a>. [Annotated scanned copy]

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,8,0,-9).

%F 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

%p A002536:=-z*(-1-z+3*z**2)/(1-8*z**2+9*z**4); [Conjectured by _Simon Plouffe_ in his 1992 dissertation.]

%t LinearRecurrence[{0,8,0,-9},{0,1,1,5},30] (* _Harvey P. Dale_, May 28 2012 *)

%K nonn,easy

%O 0,4

%A _N. J. A. Sloane_

%E Better description and more terms from _David W. Wilson_, Aug 15 1996