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%I #66 Jan 25 2023 11:47:19
%S 3,7,10,17,27,44,71,115,186,301,487,788,1275,2063,3338,5401,8739,
%T 14140,22879,37019,59898,96917,156815,253732,410547,664279,1074826,
%U 1739105,2813931,4553036,7366967,11920003,19286970,31206973,50493943,81700916,132194859
%N Fibonacci sequence beginning 3, 7.
%C From _Greg Dresden_, Feb 18 2022: (Start)
%C a(n) is also the number of ways to tile this figure, with two cells on the top row and n+1 cells on the bottom row, using squares and dominoes. Shown here are the figures for a(0) through a(4):
%C .___ .___ .___ .___ .___
%C |_|_| |_|_| |_|_|_ |_|_|___ |_|_|_____
%C |_| |_|_| |_|_|_| |_|_|_|_| |_|_|_|_|_|
%C (End)
%H Michael De Vlieger, <a href="/A022120/b022120.txt">Table of n, a(n) for n = 0..4782</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.: (3+4x)/(1-x-x^2). - _Philippe Deléham_, Nov 19 2008
%F a(n) = 4*Fibonacci(n+2) - Fibonacci(n+1). - _Gary Detlefs_, Dec 21 2010
%F a(n) = round(((15+11*sqrt(5))/10)*((1+sqrt(5))/2)^n + ((15-11*sqrt(5))/10)*((1-sqrt(5))/2)^n). - _Bogart B. Strauss_, Oct 27 2013
%F a(n) = Lucas(n+3) - Fibonacci(n-1). - _Greg Dresden_, Sam Neale, and Kyle Wood, Feb 18 2022
%F E.g.f.: exp(x/2)*(15*cosh(sqrt(5)*x/2) + 11*sqrt(5)*sinh(sqrt(5)*x/2))/5. - _Stefano Spezia_, Jul 26 2022
%t Table[4*Fibonacci[n+2]-Fibonacci[n+1],{n,0,30}] (* _Zak Seidov_, Mar 15 2011 *)
%o (PARI) v=vector(100);v[1]=3;v[2]=7;for(i=3,#v,v[i]=v[i-2]+v[i-1]);v \\ _Charles R Greathouse IV_, Mar 15 2011
%Y Cf. A000032.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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