login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A128439 a(n) = floor(n*t^n), where t=golden ratio=(1+sqrt(5))/2. 1

%I

%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.

%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

%e a(4) = floor(4*t^4).

%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. A128440.

%K nonn

%O 1,2

%A _Clark Kimberling_, Mar 03 2007

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 24 10:40 EDT 2021. Contains 348225 sequences. (Running on oeis4.)