A005821 - OEIS

A005821

a(n) = floor(tau*a(n-1)) + a(n-2) with a(0)=0 and a(1)=1.

0, 1, 1, 2, 4, 8, 16, 33, 69, 144, 301, 631, 1321, 2768, 5799, 12150, 25458, 53341, 111765, 234180, 490676, 1028110, 2154192, 4513665, 9457455, 19816148, 41520655, 86997979, 182286341, 381943474, 800283863, 1676829964, 3513451738, 7361714293, 15424955679, 32319816856

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

REFERENCES

Akhlesh Lakhtakia and Russell Messier. "Self-similar sequences and chaos from Gauss sums." Computers & graphics 13.1 (1989): 59-62. See Eq. (4b).

LINKS

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

Akhlesh Lakhtakia and Russell Messier, Self-similar sequences and chaos from Gauss sums, Computers & Graphics 13.1 (1989), 59-62. (Annotated scanned copy)

MAPLE

Digits := 20: tau := evalf( (1+sqrt(5))/2): A005821 := proc(n) option remember; if n <= 1 then n; else A005821(n-2)+floor(tau*A005821(n-1)); fi; end;

MATHEMATICA

nxt[{a_, b_}]:={b, a+Floor[b*GoldenRatio]}; NestList[nxt, {0, 1}, 30][[All, 1]] (* Harvey P. Dale, Oct 10 2017 *)

CROSSREFS

Sequence in context: A098588 A367715 A126683 * A177794 A004149 A129986

Adjacent sequences: A005818 A005819 A005820 * A005822 A005823 A005824

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved