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

1, 4, 30, 260, 2380, 22428, 215292, 2093520, 20553390, 203280220, 2022339176, 20215564824, 202879303900, 2042865050800, 20629119101400, 208829908532880, 2118554718825420, 21533269718832300, 219235457827640100, 2235446059461106800, 22824647678376163620, 233331794241184490280

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

Links

Table of n, a(n) for n=0..21.

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

Cf. A000045, A000984, A016095.

Sequence in context: A334719 A091527 A201200 * A209441 A371486 A352863

Adjacent sequences: A102304 A102305 A102306 * A102308 A102309 A102310

Keyword

nonn

Author

Ralf Stephan, Jan 03 2005

Status

approved