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A005908 a(n) = floor( phi*a(n-1) ) + floor( phi*a(n-2) ), where phi is the golden ratio. 1
0, 1, 1, 2, 4, 9, 20, 46, 106, 245, 567, 1313, 3041, 7044, 16317, 37798, 87559, 202831, 469860, 1088436, 2521375, 5840796, 13530276, 31343052, 72606569, 168194019, 389623535, 902567761, 2090809436, 4843386045 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

FORMULA

Lim n -> infinity a(n)/a(n-1) = phi / C = 2.31651242917313... where phi is the golden ratio and C the positive root of x^4+x^3-2*x^2-2*x-1 (C=0.6984784404...). - Benoit Cloitre, Aug 13 2002

Conjectures from Chai Wah Wu, Jun 13 2020: (Start)

a(n) = 2*a(n-1) + a(n-2) - a(n-4) - a(n-5) for n > 4.

G.f.: x*(-x^3 - x^2 - x + 1)/(x^5 + x^4 - x^2 - 2*x + 1). (End)

MATHEMATICA

nxt[{a_, b_}]:={b, Floor[GoldenRatio*a]+Floor[GoldenRatio*b]}; Transpose[ NestList[ nxt, {0, 1}, 30]][[1]] (* Harvey P. Dale, Apr 24 2016 *)

CROSSREFS

Cf. A001622 (golden ratio).

Sequence in context: A191653 A191827 A000968 * A206119 A085748 A317097

Adjacent sequences:  A005905 A005906 A005907 * A005909 A005910 A005911

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 14 01:26 EDT 2020. Contains 336473 sequences. (Running on oeis4.)