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A126567 Sequence generated from the E6 Cartan matrix. 2

%I

%S 1,2,5,14,42,132,430,1444,4981,17594,63441,232806,866870,3266460,

%T 12426210,47629020,183638729,711285170,2764753405,10775740030,

%U 42086252770,164635420788,644811687734,2527808259668,9916569410301

%N Sequence generated from the E6 Cartan matrix.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/E6_%28mathematics%29">E6, Mathematics</a>.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (12,-55,120,-125,52,-3).

%F Let M denote the E6 Cartan matrix [2,-1,0,0,0,0; -1,2,-1,0,0,0; 0,-1,2,-1,0,-1; 0,0,-1,2,-1,0; 0,0,0,-1,2,0; 0,0,-1,0,0,2]. a(n) = leftmost term in M^n * [1,0,0,0,0,0].

%F G.f.: -(2*x-1)*(2*x^4-16*x^3+20*x^2-8*x+1) / ((x-1)*(3*x-1)*(x^4-16*x^3+20*x^2-8*x+1)). - _Colin Barker_, May 25 2013

%e a(6) = 430 since leftmost term of M^6 * [1,0,0,0,0,0] = 430.

%t f[n_] := (MatrixPower[{{2, -1, 0, 0, 0, 0}, {-1, 2, -1, 0, 0, 0}, {0, -1, 2, -1, 0, -1}, {0, 0, -1, 2, -1, 0}, {0, 0, 0, -1, 2, 0}, {0, 0, -1, 0, 0, 2}}, n].{1, 0, 0, 0, 0, 0})[[1]]; Table[ f@n, {n, 0, 25}] - _Robert G. Wilson v_, Aug 07 2007

%Y Cf. A126566, A126568, A126569.

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Dec 28 2006

%E More terms from _Robert G. Wilson v_, Aug 07 2007

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Last modified October 16 19:22 EDT 2018. Contains 316271 sequences. (Running on oeis4.)