A139333 - OEIS

%I #3 Apr 05 2012 18:27:14

%S 1,1,3,7,15,32,68,144,302,633,1328,2783,5832,12219,25604,53648,112408,

%T 235529,493503,1034034,2166605,4539675,9511953,19930339,41759920,

%U 87499309,183336777

%N Floor of entry (2,1) of [0,1; 1,phi]^n.

%C a(n)/a(n-1) tends to 2.095293... = exp ArcSinh(phi/2).

%F Floor of entry (2,1) and (1,2) of [0,1; 1,phi]^n. Floor numerators of barover[phi] = [phi, phi, phi,...] where phi = 1.618033989...

%e a(5) = 15 since [0,1, 1,phi]^5 = [7.472...,15.708...; 15.708...,32.888...].

%e a(5) = 15 = floor 15.708203..., since the first five numerators of continued fraction[phi, phi, phi, phi, phi,...] = [1, phi, (phi^2 + 1), (phi^3 + 2*phi), (phi^4 + 3*phi^2 + 1), where (phi^4 + 3*phi^2 + 1) = 15.708203...

%K nonn

%O 1,3

%A _Gary W. Adamson_ and _Roger L. Bagula_, Apr 13 2008