A005821 a(n) = [ tau*a(n-1) ] + a(n-2).

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

Offset

0,4

References

Lakhtakia, Akhlesh, 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

A. Lakhtakia & R. 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