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

0,2

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

Table of n, a(n) for n=0..104.

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

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

Mathematica

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

Prog

(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
(Magma) [4^n mod 12: n in [0..40]]; // Vincenzo Librandi, Apr 23 2015
(Maxima) makelist(if n=0 then 1 else 4, n, 0, 100); /* Bruno Berselli, Apr 24 2015 */

Crossrefs

Sequence in context: A088848 A088849 A251539 * A010709 A138908 A032564

Adjacent sequences: A123929 A123930 A123931 * A123933 A123934 A123935

Keyword

nonn,cofr,easy

Author

Philippe Deléham, Nov 28 2006

Status

approved