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A005821
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a(n) = [ tau*a(n-1) ] + a(n-2).
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3
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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
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OFFSET
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0,4
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REFERENCES
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Lakhtakia, Akhlesh, and Russell Messier. "Self-similar sequences and chaos from Gauss sums." Computers & graphics 13.1 (1989): 59-62. See Eq. (4b).
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LINKS
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MAPLE
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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;
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MATHEMATICA
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nxt[{a_, b_}]:={b, a+Floor[b*GoldenRatio]}; NestList[nxt, {0, 1}, 30][[All, 1]] (* Harvey P. Dale, Oct 10 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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