A062724 a(n) = floor(tau^n) + 1, where tau = (1 + sqrt(5))/2.

2, 2, 3, 5, 7, 12, 18, 30, 47, 77, 123, 200, 322, 522, 843, 1365, 2207, 3572, 5778, 9350, 15127, 24477, 39603, 64080, 103682, 167762, 271443, 439205, 710647, 1149852, 1860498, 3010350, 4870847, 7881197, 12752043, 20633240, 33385282

Offset: 0

Author

Jason Earls, Jul 15 2001

Keywords

• nonn

Comments

Apart from the first term, this sequence also gives the ceiling of the powers of the golden ratio (cf. A169986). - Mohammad K. Azarian, Apr 14 2008

Links

• Harry J. Smith, Table of n, a(n) for n = 0..400

Crossrefs

Equals A014217 + 1.

Cf. A169985, A169986.

Programs

Mathematica

Floor[GoldenRatio^Range[0,40]]+1 (* Harvey P. Dale, Dec 18 2019 *)

PARI

j=[]; for(n=0,60,t=(1+sqrt(5))/2; j=concat(j,floor((t^n))+1)); j

PARI

{ default(realprecision, 200); t=(1 + sqrt(5))/2; p=1; for (n=0, 400, if (n, p*=t); write("b062724.txt", n, " ", p\1 + 1) ) } \\ Harry J. Smith, Aug 09 2009

Formula

a(n) = 3*Fibonacci(n-1) + Fibonacci(n-2) + (n mod 2), n > 0. - Gary Detlefs, Dec 29 2010