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A102307 a(n) = Fibonacci(2n+1) * binomial(2n,n).

%I A102307 #30 Apr 30 2024 02:11:37
%S A102307 1,4,30,260,2380,22428,215292,2093520,20553390,203280220,2022339176,
%T A102307 20215564824,202879303900,2042865050800,20629119101400,
%U A102307 208829908532880,2118554718825420,21533269718832300,219235457827640100,2235446059461106800,22824647678376163620,233331794241184490280
%N A102307 a(n) = Fibonacci(2n+1) * binomial(2n,n).
%C A102307 Central column of triangle A016095.
%C A102307 a(n) is the number of ways to tile a strip of length 2n with squares labeled 0 or 1, and dominoes labeled 00, 01, 10, or 11, where there are in total n 0's and n 1's in the tiling. - _Greg Dresden_ and _Yiming Tan_, Aug 15 2020
%F A102307 a(n) = Fibonacci(2n+1) * binomial(2n,n) = A000045(2n+1) * A000984(n). - _Philippe Deléham_, Oct 14 2006
%F A102307 a(n) = A016095(n,n).
%F A102307 Sum_{n>=0} a(n)/16^n = 2*sqrt(10+2*sqrt(5))/5. - _Amiram Eldar_, May 06 2023
%F A102307 G.f.: sqrt(3-8*x+2*sqrt(1-12*x+16*x^2))/(sqrt(5)*sqrt(1-12*x+16*x^2)). - _Vladimir Kruchinin_, Apr 30 2024
%e A102307 a(0) = F(1)*C(0,0) = 1*1 = 1;
%e A102307 a(1) = F(3)*C(2,1) = 2*2 = 4;
%e A102307 a(2) = F(5)*C(4,2) = 5*6 = 30;
%e A102307 a(3) = F(7)*C(6,3) = 13*20 = 260; ...
%t A102307 Table[Fibonacci[2n+1]Binomial[2n,n],{n,0,20}] (* _Harvey P. Dale_, Aug 03 2016 *)
%o A102307 (PARI) a(n)=fibonacci(2*n+1)*binomial(2*n,n)
%Y A102307 Cf. A000045, A000984, A016095.
%K A102307 nonn
%O A102307 0,2
%A A102307 _Ralf Stephan_, Jan 03 2005