A128439 a(n) = floor(n*t^n), where t=golden ratio=(1+sqrt(5))/2.

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

Offset: 1

Author

Clark Kimberling, Mar 03 2007

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,2,-4,-2,2,1).

Crossrefs

Cf. A000045, A128440.

Programs

Mathematica

Table[Floor[n*GoldenRatio^n], {n, 50}] (* Indranil Ghosh, Apr 18 2017 *)

PARI

a(n) = floor(n*((1 + sqrt(5))/2)^n); \\ Indranil Ghosh, Apr 18 2017

Formula

a(n) = A128440(n, n).

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