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
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
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
KEYWORD
nonn,cofr,easy
AUTHOR
Philippe Deléham, Nov 28 2006
STATUS
approved