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%I #19 Oct 15 2017 21:49:08
%S 0,1,1,2,4,8,16,33,69,144,301,631,1321,2768,5799,12150,25458,53341,
%T 111765,234180,490676,1028110,2154192,4513665,9457455,19816148,
%U 41520655,86997979,182286341,381943474
%N a(n) = [ tau*a(n-1) ] + a(n-2).
%D Lakhtakia, Akhlesh, and Russell Messier. "Self-similar sequences and chaos from Gauss sums." Computers & graphics 13.1 (1989): 59-62. See Eq. (4b).
%H Harvey P. Dale, <a href="/A005821/b005821.txt">Table of n, a(n) for n = 0..1000</a>
%H A. Lakhtakia & R. Messier, <a href="/A005821/a005821.pdf">Self-similar sequences and chaos from Gauss sums</a>, Computers & Graphics 13.1 (1989), 59-62. (Annotated scanned copy)
%p 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;
%t nxt[{a_,b_}]:={b,a+Floor[b*GoldenRatio]}; NestList[nxt,{0,1},30][[All,1]] (* _Harvey P. Dale_, Oct 10 2017 *)
%K nonn
%O 0,4
%A _N. J. A. Sloane_.
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