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%I #38 Jun 07 2023 08:31:44
%S 5,13,18,31,49,80,129,209,338,547,885,1432,2317,3749,6066,9815,15881,
%T 25696,41577,67273,108850,176123,284973,461096,746069,1207165,1953234,
%U 3160399,5113633,8274032,13387665,21661697,35049362,56711059,91760421,148471480
%N Fibonacci sequence beginning 5, 13.
%C From _Greg Dresden_ and _Wajdi Maaloul_, Jun 19 2022: (Start)
%C a(n) is the number of ways to tile this strip of length n+4 (with a bump in the n=5 position) using squares and dominos.
%C . _
%C ._______|_|_________ _
%C |_|_|_|_|_|_|_|_|_|_|...|_|
%C (End)
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F a(0) = 5, a(1) = 13, a(n) = a(n - 2) + a(n - 1).
%F G.f.: (5 + 8x)/(1 - x - x^2). - _Philippe Deléham_, Nov 20 2008
%F E.g.f.: exp(x/2)*(25*cosh(sqrt(5)*x/2) + 21*sqrt(5)*sinh(sqrt(5)*x/2))/5. - _Stefano Spezia_, Jun 06 2023
%t LinearRecurrence[{1, 1}, {5, 13}, 50] (* _Harvey P. Dale_, Jul 10 2017 *)
%t CoefficientList[Series[(5 + 8x)/(1 - x - x^2), {x, 0, 50}], x] (* _Stefano Spezia_, Oct 11 2018 *)
%Y Cf. A000032, A000045.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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