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A128439
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a(n) = floor(n*t^n), where t=golden ratio=(1+sqrt(5))/2.
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2
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1, 5, 12, 27, 55, 107, 203, 375, 684, 1229, 2189, 3863, 6773, 11801, 20460, 35311, 60707, 104003, 177631, 302539, 513996, 871265, 1473817, 2488367, 4194025, 7057517, 11858508, 19898115, 33345679, 55814939, 93320819, 155867103
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = n*F(n-1) + floor(n*t*F(n)), where F=A000045, the Fibonacci numbers.
G.f.: x*(1 + 3*x - 3*x^3 - x^4 - x^5)/((1 - x)*(1 + x)*(1 - x - x^2)^2). - Ilya Gutkovskiy, Apr 18 2017
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MATHEMATICA
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Table[Floor[n*GoldenRatio^n], {n, 50}] (* Indranil Ghosh, Apr 18 2017 *)
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PROG
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(PARI) a(n) = floor(n*((1 + sqrt(5))/2)^n); \\ Indranil Ghosh, Apr 18 2017
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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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