

A214733


a(n) =  a(n1)  3*a(n2), with a(0) = 0 and a(1) = 1.


3



0, 1, 1, 2, 5, 1, 16, 13, 35, 74, 31, 253, 160, 599, 1079, 718, 3955, 1801, 10064, 15467, 14725, 61126, 16951, 166427, 217280, 282001, 933841, 87838, 2713685, 2977199, 5163856, 14095453, 1396115, 43682474, 39494129, 91553293, 210035680
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OFFSET

0,4


COMMENTS

The sequence a(n) is conjugate with A110523 by the following alternative relations: either ((1 + i*sqrt(11))/2)^n = A110523(n) + a(n)*(1 + i*sqrt(11))/2, or ((1  i*sqrt(11))/2)^n = A110523(n) + a(n)*(1  i*sqrt(11))/2 (see also comments to A110523, where these relations and many other facts on a(n) is presented).
Apart from signs, the Lucas U(P=1,Q=3)sequence.  R. J. Mathar, Oct 24 2012


REFERENCES

R. Witula, On Some Applications of Formulae for Unimodular Complex Numbers, Jacek Skalmierski's Press, Gliwice 2011.


LINKS

Table of n, a(n) for n=0..36.
Wikipedia, Lucas sequence


FORMULA

a(n+2) =  a(n+1)  3a(n).
a(n) = (i*sqrt(11)/11)*(((1  i*sqrt(11))/2)^n  ((1 + i*sqrt(11))/2)^n).
G.f.: x/(1 + x + 3*x^2).
G.f.: Q(0) 1, where Q(k) = 1  3*x^2  (k+2)*x + x*(k+1 + 3*x)/Q(k+1); (continued fraction).  Sergei N. Gladkovskii, Oct 07 2013


MATHEMATICA

LinearRecurrence[{1, 3}, {0, 1}, 40] (* T. D. Noe, Jul 30 2012 *)


PROG

(PARI) concat(0, Vec(1/(1+x+3*x^2)+O(x^99))) \\ Charles R Greathouse IV, Oct 01 2012


CROSSREFS

Cf. A106852, A110523.
Sequence in context: A186361 A197365 A121579 * A106852 A162975 A187244
Adjacent sequences: A214730 A214731 A214732 * A214734 A214735 A214736


KEYWORD

sign,easy


AUTHOR

Roman Witula, Jul 27 2012


STATUS

approved



