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A169986
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Ceiling(phi^n) where phi = (1+sqrt(5))/2.
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7
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1, 2, 3, 5, 7, 12, 18, 30, 47, 77, 123, 200, 322, 522, 843, 1365, 2207, 3572, 5778, 9350, 15127, 24477, 39603, 64080, 103682, 167762, 271443, 439205, 710647, 1149852, 1860498, 3010350, 4870847, 7881197, 12752043, 20633240, 33385282
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 3*Fibonacci(n-1) + Fibonacci(n-2) + (n mod 2), n>0. - Gary Detlefs, Dec 29 2010
G.f.: (-x+x^2+x^3+x^4-1) / ((1-x)*(1+x)*(x^2+x-1)). - R. J. Mathar, Jan 06 2011
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MATHEMATICA
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Ceiling[GoldenRatio^Range[0, 40]] (* or *) Join[{1}, LinearRecurrence[{1, 2, -1, -1}, {2, 3, 5, 7}, 40]] (* Harvey P. Dale, Nov 12 2014 *)
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PROG
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(Magma) [1] cat [3*Fibonacci(n-1) + Fibonacci(n-2)+ n mod 2: n in [1..40]]; // Vincenzo Librandi, Apr 16 2015
(Sage) [ceil(golden_ratio^n) for n in range(37)] # Danny Rorabaugh, Apr 16 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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