A350092 a(n) = floor(x^n) where x = 1 + sqrt(5)/2 = A176055.

1, 2, 4, 9, 20, 42, 90, 191, 405, 857, 1816, 3848, 8150, 17263, 36564, 77445, 164031, 347423, 735855, 1558567, 3301098, 6991839, 14808952, 31365865, 66433969, 140709405, 298027302, 631231956, 1336970739, 2831749467, 5997741619, 12703420605, 26906276616

Offset: 0

Author

Michel Lagneau, Dec 14 2021

Keywords

• nonn
• easy

Comments

a(n+1)/a(n) tends to A176055 when n tends towards infinity.

Crossrefs

Cf. A176055, A058066 (x*n), A014217 (phi^n).

Programs

Maple

seq(floor((1+sqrt(5)/2)^n), n=0..32);

Mathematica

a[n_] := Floor[(GoldenRatio + 1/2)^n]; Array[a, 33, 0] (* Amiram Eldar, Dec 14 2021 *)

Python

from sympy import floor, sqrt
def A350092(n): return floor((1+sqrt(5)/2)**n) # Chai Wah Wu, Dec 17 2021