VOOZH about

URL: https://oeis.org/A130815

⇱ A130815 - OEIS

login
A130815
Period 6: repeat [1, 5, 4, -1, -5, -4].
5
1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4
OFFSET
0,2
COMMENTS
Continued fraction expansion of (5+sqrt(11))/7 = 1.1880892557650... - R. J. Mathar, Mar 08 2012
FORMULA
Binomial transform of 1, 4, -5.
From R. J. Mathar, Oct 30 2008: (Start)
G.f.: (1+4*x)/(1-x+x^2).
a(n) = A010892(n) + 4*A010892(n-1). (End)
From Wesley Ivan Hurt, Jun 17 2016: (Start)
a(n) = a(n-1) - a(n-2) for n>1.
a(n) = cos(n*Pi/3) + 3*sqrt(3)*sin(n*Pi/3). (End)
E.g.f.: exp(x/2) * (cos(sqrt(3)*x/2) + 3*sqrt(3)*sin(sqrt(3)*x/2)). - Amiram Eldar, Dec 07 2025
MATHEMATICA
Flatten[Table[{1, 5, 4, -1, -5, -4}, {20}]] (* Wesley Ivan Hurt, Jun 17 2016 *)
PadRight[{}, 120, {1, 5, 4, -1, -5, -4}] (* Harvey P. Dale, Jul 12 2020 *)
PROG
(PARI) a(n)=[1, 5, 4, -1, -5, -4][n%6+1] \\ Charles R Greathouse IV, Jun 02 2011
(Magma) &cat[[1, 5, 4, -1, -5, -4]: n in [0..20]]; // Wesley Ivan Hurt, Jun 17 2016
CROSSREFS
Cf. A010892.
Sequence in context: A198352 A113011 A028875 * A342797 A084129 A011503
KEYWORD
sign,easy,less
AUTHOR
Paul Curtz, Jul 16 2007
EXTENSIONS
Edited by N. J. A. Sloane, Sep 15 2007
STATUS
approved