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 A172128 a(n) = floor(phi^n/n), where phi = golden ratio = (1+sqrt(5))/2. 3
 1, 1, 1, 1, 2, 2, 4, 5, 8, 12, 18, 26, 40, 60, 90, 137, 210, 320, 492, 756, 1165, 1800, 2786, 4320, 6710, 10440, 16266, 25380, 39650, 62016, 97108, 152213, 238824, 375060, 589521, 927368, 1459960, 2300100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS G. C. Greubel, Table of n, a(n) for n = 1..4500 FORMULA a(n) = floor((1/n)*(Fibonacci(n)*phi + Fibonacci(n-1)), where phi = (1+sqrt(5))/2. MATHEMATICA Table[Floor[((1 + Sqrt[5])/2)^n/n], {n, 1, 50}] Table[Floor[GoldenRatio^n/n], {n, 50}] (* Harvey P. Dale, Dec 12 2018 *) PROG (Magma) [Floor((Lucas(n) + Sqrt(5)*Fibonacci(n))/(2*n)): n in [1..50]]; // G. C. Greubel, Apr 17 2022 (SageMath) [floor(golden_ratio^n/n) for n in (1..50)] # G. C. Greubel, Apr 17 2022 CROSSREFS Cf. A000045, A001622 (phi), A181885. Sequence in context: A050364 A078465 A094992 * A274154 A274153 A079501 Adjacent sequences: A172125 A172126 A172127 * A172129 A172130 A172131 KEYWORD nonn AUTHOR Clark Kimberling, Nov 20 2010 STATUS approved

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Last modified December 3 19:10 EST 2023. Contains 367540 sequences. (Running on oeis4.)