|
%I #13 Feb 02 2020 14:57:25
%S 1,3,10,25,60,133,284,585,1175,2310,4464,8502,15995,29775,54920,
%T 100487,182556,329555,591550,1056405,1877821,3323868,5860800,10297500,
%U 18033925,31487643,54824854,95211205,164948700
%N Row sums of triangle A067330; also of triangle A067418.
%C 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
%F a(n)= (n+2)*((3*n+5)*F(n+1)+(n+1)*F(n))/10, with F(n) := A000045(n) (Fibonacci).
%F G.f.: (1+x^2)/(1-x-x^2)^3.
%F Sum_{j=0..n} binomial(n-j,j)*n*j/2. - _Zerinvary Lajos_, Oct 19 2006
%p a:=n->sum(binomial(n-j,j)*n*j/2,j=0..n): seq(a(n), n=2..30); # _Zerinvary Lajos_, Oct 19 2006
%t Table[((n+2)((3n+5)Fibonacci[n+1]+(n+1)Fibonacci[n]))/10,{n,0,30}] (* _Harvey P. Dale_, Feb 02 2020 *)
%Y Cf. A001628.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Feb 15 2002
|
