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A139333 Floor of entry (2,1) of [0,1; 1,phi]^n. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A132978 A117079 A026745 * A099444 A132402 A137166

Adjacent sequences:  A139330 A139331 A139332 * A139334 A139335 A139336

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified May 25 05:45 EDT 2019. Contains 323539 sequences. (Running on oeis4.)