# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a002536 Showing 1-1 of 1 %I A002536 M3783 N1540 #48 Oct 17 2023 05:44:17 %S A002536 0,1,1,5,8,31,55,203,368,1345,2449,8933,16280,59359,108199,394475, %T A002536 719072,2621569,4778785,17422277,31758632,115784095,211059991, %U A002536 769472267,1402652240,5113721281,9321678001,33984519845,61949553848,225852667231 %N A002536 a(n) = 8*a(n-2) - 9*a(n-4). %D A002536 Murat Sahin and Elif Tan, Conditional (strong) divisibility sequences, Fib. Q., 56 (No. 1, 2018), 18-31. %D A002536 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). %D A002536 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %D A002536 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 A002536 Harvey P. Dale, Table of n, a(n) for n = 0..1000 %H A002536 Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009. %H A002536 Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 %H A002536 Albert Tarn, Approximations to certain square roots and the series of numbers connected therewith. [Annotated scanned copy] %H A002536 Index entries for linear recurrences with constant coefficients, signature (0,8,0,-9). %F A002536 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 A002536:=-z*(-1-z+3*z**2)/(1-8*z**2+9*z**4); [Conjectured by _Simon Plouffe_ in his 1992 dissertation.] %t A002536 LinearRecurrence[{0,8,0,-9},{0,1,1,5},30] (* _Harvey P. Dale_, May 28 2012 *) %K A002536 nonn,easy %O A002536 0,4 %A A002536 _N. J. A. Sloane_ %E A002536 Better description and more terms from _David W. Wilson_, Aug 15 1996 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE