A038213 Top line of 3-wave sequence A038196, also bisection of A006356.

1, 3, 14, 70, 353, 1782, 8997, 45425, 229347, 1157954, 5846414, 29518061, 149034250, 752461609, 3799116465, 19181424995, 96845429254, 488964567014, 2468741680809, 12464472679038, 62932092237197, 317738931708801

Offset

0,2

Links

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

Johann Cigler, Number of bounded Dyck paths with "negative length", MathOverflow question, Sep 26 2020.

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