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%I #18 Jun 15 2022 11:37:17
%S 1,5,12,27,55,107,203,375,684,1229,2189,3863,6773,11801,20460,35311,
%T 60707,104003,177631,302539,513996,871265,1473817,2488367,4194025,
%U 7057517,11858508,19898115,33345679,55814939,93320819,155867103
%N a(n) = floor(n*t^n), where t=golden ratio=(1+sqrt(5))/2.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-4,-2,2,1).
%F a(n) = A128440(n, n).
%F a(n) = n*F(n-1) + floor(n*t*F(n)), where F=A000045, the Fibonacci numbers.
%F 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
%t Table[Floor[n*GoldenRatio^n], {n, 50}] (* _Indranil Ghosh_, Apr 18 2017 *)
%o (PARI) a(n) = floor(n*((1 + sqrt(5))/2)^n); \\ _Indranil Ghosh_, Apr 18 2017
%Y Cf. A000045, A128440.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Mar 03 2007
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