OFFSET
0,4
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
FORMULA
Limit_{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
KEYWORD
nonn
AUTHOR
STATUS
approved