A123932 a(0) = 1, a(n) = 4 for n > 0.

1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 0

Author

Philippe Deléham, Nov 28 2006

Keywords

• nonn
• cofr
• easy

Comments

Continued fraction for sqrt(5)-1.

a(n) = number of permutations of length n+3 having only one ascent such that the first element of the permutation is 3. - Ran Pan, Apr 20 2015

Also, decimal expansion of 13/90. - Bruno Berselli, Apr 24 2015

Column 1 of A327331 and of A327333. - Omar E. Pol, Nov 25 2019

Links

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

Crossrefs

Essentially the same as A113311, A040002 and A010709.

Programs

Magma

[4^n mod 12: n in [0..40]]; // Vincenzo Librandi, Apr 23 2015

Mathematica

ContinuedFraction[Sqrt[5] - 1, 120] (* Michael De Vlieger, Apr 20 2015 *)

Maxima

makelist(if n=0 then 1 else 4, n, 0, 100); /* Bruno Berselli, Apr 24 2015 */

PARI

a(n)=(n>=0)+3*(n>0) \\ Jaume Oliver Lafont, Mar 26 2009

Sage

[power_mod(4, n, 12) for n in range(0, 84)] # Zerinvary Lajos, Nov 25 2009

Formula

G.f.: (1 + 3*x) / (1 - x).

a(n) = 4 - 3*0^n .

a(n) = 4^n mod 12. - Zerinvary Lajos, Nov 25 2009

E.g.f.: 4*exp(x) - 3. - Elmo R. Oliveira, Aug 06 2024