A038223 Bottom line of 3-wave sequence A038196, also bisection of A006356.

1, 6, 31, 157, 793, 4004, 20216, 102069, 515338, 2601899, 13136773, 66326481, 334876920, 1690765888, 8536537209, 43100270734, 217609704247, 1098693409021, 5547212203625, 28007415880892, 141407127676248

Offset

0,2

Comments

Suggested by the Steinbach heptagon polynomial p^3 - p^2*(1 - p) - 2*p(1 - p)^2 + (1 - p)^3 = (1 - 5 p + 6 p^2 - p^3). - Roger L. Bagula, Sep 20 2006

Links

Table of n, a(n) for n=0..20.

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]. - From N. J. A. Sloane, Dec 26 2012

F. v. Lamoen, Wave sequences

P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.

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), so M(3)=(1, 1, 1)/(1, 2, 2)/(1, 2, 3); then a(n)= Max ( v(3)*M(3)^n) - Benoit Cloitre, Oct 03 2002

G.f.: 1/(1-6x+5x^2-x^3). - Roger L. Bagula and Gary W. Adamson, Sep 20 2006

Mathematica

p[x_] := 1 - 5 x + 6 x^2 - x^3; q[x_] := ExpandAll[x^3*p[1/x]]; Table[ SeriesCoefficient[ Series[x/q[x], {x, 0, 30}], n], {n, 0, 30}] (* Roger L. Bagula, Sep 20 2006 *)

Prog

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

Crossrefs

Sequence in context: A289788 A065096 A077352 * A334650 A022034 A277669

Adjacent sequences: A038220 A038221 A038222 * A038224 A038225 A038226

Keyword

nonn,easy

Author

Floor van Lamoen

Extensions

More terms from Benoit Cloitre, Oct 03 2002

Edited by R. J. Mathar, Aug 02 2008

Status

approved