OFFSET
0,2
COMMENTS
a(n) is the sum of the positions of the 0's in all Fibonacci binary words of length n+1. A Fibonacci binary word is a binary word having no 00 subword. Example: a(3)=25 because the Fibonacci binary words of length 4 are 1110, 1111, 1101, 1010, 1011, 0110, 0111 and 0101, the positions of the 0's being 4, 3, 2, 4, 2, 1, 4, 1, 1 and 3 (their sum is 25). - Emeric Deutsch, Jan 04 2009
FORMULA
a(n)= (n+2)*((3*n+5)*F(n+1)+(n+1)*F(n))/10, with F(n) := A000045(n) (Fibonacci).
G.f.: (1+x^2)/(1-x-x^2)^3.
Sum_{j=0..n} binomial(n-j,j)*n*j/2. - Zerinvary Lajos, Oct 19 2006
MAPLE
a:=n->sum(binomial(n-j, j)*n*j/2, j=0..n): seq(a(n), n=2..30); # Zerinvary Lajos, Oct 19 2006
MATHEMATICA
Table[((n+2)((3n+5)Fibonacci[n+1]+(n+1)Fibonacci[n]))/10, {n, 0, 30}] (* Harvey P. Dale, Feb 02 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Feb 15 2002
STATUS
approved