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
Links
- 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).
Programs
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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 *) -
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)
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
Extensions
More terms from Benoit Cloitre, Oct 03 2002
Edited by R. J. Mathar, Aug 02 2008
Comments