A139333 Floor of entry (2,1) of [0,1; 1,phi]^n.

1, 1, 3, 7, 15, 32, 68, 144, 302, 633, 1328, 2783, 5832, 12219, 25604, 53648, 112408, 235529, 493503, 1034034, 2166605, 4539675, 9511953, 19930339, 41759920, 87499309, 183336777

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..27.

Formula

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...

Example

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

Crossrefs

Sequence in context: A368346 A117079 A026745 * A099444 A374678 A132402

Adjacent sequences: A139330 A139331 A139332 * A139334 A139335 A139336

Keyword

nonn

Author

Gary W. Adamson and Roger L. Bagula, Apr 13 2008

Status

approved