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A038213 Top line of 3-wave sequence A038196, also bisection of A006356. 1
1, 3, 14, 70, 353, 1782, 8997, 45425, 229347, 1157954, 5846414, 29518061, 149034250, 752461609, 3799116465, 19181424995, 96845429254, 488964567014, 2468741680809, 12464472679038, 62932092237197, 317738931708801 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

S. Morier-Genoud, V. Ovsienko and S. Tabachnikov, 2-frieze patterns and the cluster structure of the space of polygons, Annales de l'institut Fourier, 62 no. 3 (2012), 937-987; arXiv:1008.3359 [math.AG], 2010-2011. - N. J. A. Sloane, Dec 26 2012

F. v. Lamoen, Wave sequences

Index entries for linear recurrences with constant coefficients, signature (6, -5, 1).

FORMULA

Let v(3)=(1, 1, 1), let M(3) be the 3 X 3 matrix m(i, j) =min(i, j); then a(n)= min ( v(3)*M(3)^n). - Benoit Cloitre, Oct 03 2002

G.f.: -((1 + (-3 + q)*q)/(-1 + (-3 + q)*(-2 + q)*q)). - Wouter Meeussen, Mar 19 2005

G.f.: (1 - 3*x + x^2) / (1 - 6*x + 5*x^2 - x^3).

a(-n) = A080937(n) for all n in Z. a(n + 2) * a(n) - a(n + 1)^2 = a(-3 - n) for all n in Z. - Michael Somos, May 04 2012

EXAMPLE

G.f. = 1 + 3*x + 14*x^2 + 70*x^3 + 353*x^4 + 1782*x^5 + 8997*x^6 + 45425*x^7 + ...

PROG

(PARI) k=3; M(k)=matrix(k, k, i, j, min(i, j)); v(k)=vector(k, i, 1); a(n)=vecmin(v(k)*M(k)^n)

(PARI) {a(n) = if( n<0, n = -n; polcoeff( (1 - 4*x + 3*x^2) / (1 - 5*x + 6*x^2 - x^3) + x * O(x^n), n), polcoeff( (1 - 3*x + x^2) / (1 - 6*x + 5*x^2 - x^3) + x * O(x^n), n))}; /* Michael Somos, May 04 2012 */

CROSSREFS

Cf. A080937.

Sequence in context: A151325 A020065 A028938 * A261207 A161939 A270598

Adjacent sequences:  A038210 A038211 A038212 * A038214 A038215 A038216

KEYWORD

nonn,easy

AUTHOR

Floor van Lamoen

EXTENSIONS

More terms from Benoit Cloitre, Oct 03 2002

STATUS

approved

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Last modified July 30 04:51 EDT 2021. Contains 346348 sequences. (Running on oeis4.)