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 A169986 Ceiling(phi^n) where phi = (1+sqrt(5))/2. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Danny Rorabaugh, Table of n, a(n) for n = 0..4000 Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-1). FORMULA For n >= 5, a(n) = a(n-1) + 2a(n-2) - a(n-3) - a(n-4). - Charles R Greathouse IV, Oct 14 2010 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 a(2k) = A000032(2k) = A169985(2k) and a(2k+1) = A000032(2k+1)+1 = A169985(2k+1)+1, for k>0. - Danny Rorabaugh, Apr 15 2015 MATHEMATICA Ceiling[GoldenRatio^Range[0, 40]] (* or *) Join[{1}, LinearRecurrence[{1, 2, -1, -1}, {2, 3, 5, 7}, 40]] (* Harvey P. Dale, Nov 12 2014 *) PROG (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 (PARI) a(n)=if(n, 3*fibonacci(n-1) + fibonacci(n-2) + n%2, 1) \\ Charles R Greathouse IV, Apr 16 2015 CROSSREFS Cf. A001622, A014217, A062724, A169985. Sequence in context: A239915 A013983 A257863 * A218021 A137713 A326490 Adjacent sequences:  A169983 A169984 A169985 * A169987 A169988 A169989 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Sep 26 2010 STATUS approved

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Last modified June 14 19:28 EDT 2021. Contains 345038 sequences. (Running on oeis4.)