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Fibonacci sequence beginning 4, 10.
4

%I #43 Jun 15 2022 01:53:00

%S 4,10,14,24,38,62,100,162,262,424,686,1110,1796,2906,4702,7608,12310,

%T 19918,32228,52146,84374,136520,220894,357414,578308,935722,1514030,

%U 2449752,3963782,6413534,10377316,16790850,27168166,43959016,71127182,115086198,186213380

%N Fibonacci sequence beginning 4, 10.

%C From _Reeva Bohra_ and _Greg Dresden_, Aug 17 2021: (Start)

%C For n > 0, a(n) is the number of ways to tile, with squares and dominoes, a strip of length n+1 that begins with two vertical strips of heights 3 and 2. As an example, a(5) is the number of ways to tile this figure (of length 6) with squares and dominoes.

%C ._

%C |_|_

%C |_|_|_______

%C |_|_|_|_|_|_|

%C (End)

%H Michael De Vlieger, <a href="/A022382/b022382.txt">Table of n, a(n) for n = 0..4781</a>

%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 G.f.: (4+6x)/(1-x-x^2). - _Philippe Deléham_, Nov 19 2008

%F a(n) = 2*A001060(n). - _R. J. Mathar_, Mar 11 2011

%F a(n) = Fibonacci(n+5) + Lucas(n-1). - _Greg Dresden_, Feb 18 2022

%F a(n) = a(n-1) + a(n-2). - _Wesley Ivan Hurt_, Mar 08 2022

%t LinearRecurrence[{1, 1}, {4, 10}, 50] (* _Greg Dresden_, Aug 17 2021 *)

%Y Cf. A001060, A022124.

%K nonn

%O 0,1

%A _N. J. A. Sloane_