cp's OEIS Frontend

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

%I A038223 #25 Sep 18 2015 12:31:19
%S A038223 1,6,31,157,793,4004,20216,102069,515338,2601899,13136773,66326481,
%T A038223 334876920,1690765888,8536537209,43100270734,217609704247,
%U A038223 1098693409021,5547212203625,28007415880892,141407127676248
%N A038223 Bottom line of 3-wave sequence A038196, also bisection of A006356.
%C A038223 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
%H A038223 S. Morier-Genoud, V. Ovsienko and S. Tabachnikov, <a href="http://arxiv.org/abs/1008.3359">2-frieze patterns and the cluster structure of the space of polygons</a>, Annales de l'institut Fourier, 62 no. 3 (2012), 937-987; arXiv:1008.3359 [math.AG]. - From _N. J. A. Sloane_, Dec 26 2012
%H A038223 F. v. Lamoen, <a href="http://home.wxs.nl/~lamoen/wiskunde/wave.htm">Wave sequences</a>
%H A038223 P. Steinbach, <a href="http://www.jstor.org/stable/2691048">Golden fields: a case for the heptagon</a>, Math. Mag. 70 (1997), no. 1, 22-31.
%H A038223 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5,1).
%F A038223 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
%F A038223 G.f.: 1/(1-6x+5x^2-x^3). - _Roger L. Bagula_ and _Gary W. Adamson_, Sep 20 2006
%t A038223 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 *)
%o A038223 (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)
%K A038223 nonn,easy
%O A038223 0,2
%A A038223 _Floor van Lamoen_
%E A038223 More terms from _Benoit Cloitre_, Oct 03 2002
%E A038223 Edited by _R. J. Mathar_, Aug 02 2008