OFFSET
0,2
COMMENTS
Central column of triangle A016095.
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
FORMULA
a(n) = Fibonacci(2n+1) * binomial(2n,n) = A000045(2n+1) * A000984(n). - Philippe Deléham, Oct 14 2006
a(n) = A016095(n,n).
Sum_{n>=0} a(n)/16^n = 2*sqrt(10+2*sqrt(5))/5. - Amiram Eldar, May 06 2023
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
EXAMPLE
a(0) = F(1)*C(0,0) = 1*1 = 1;
a(1) = F(3)*C(2,1) = 2*2 = 4;
a(2) = F(5)*C(4,2) = 5*6 = 30;
a(3) = F(7)*C(6,3) = 13*20 = 260; ...
MATHEMATICA
Table[Fibonacci[2n+1]Binomial[2n, n], {n, 0, 20}] (* Harvey P. Dale, Aug 03 2016 *)
PROG
(PARI) a(n)=fibonacci(2*n+1)*binomial(2*n, n)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Stephan, Jan 03 2005
STATUS
approved