

A123932


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


5



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
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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


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 xrange(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



