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A126567 Sequence generated from the E6 Cartan matrix. 2
1, 2, 5, 14, 42, 132, 430, 1444, 4981, 17594, 63441, 232806, 866870, 3266460, 12426210, 47629020, 183638729, 711285170, 2764753405, 10775740030, 42086252770, 164635420788, 644811687734, 2527808259668, 9916569410301 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

Wikipedia, E6, Mathematics.

Index entries for linear recurrences with constant coefficients, signature (12,-55,120,-125,52,-3).

FORMULA

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].

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

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

Cf. A126566, A126568, A126569.

Sequence in context: A168491 A000108 A057413 * A125501 A126569 A162748

Adjacent sequences:  A126564 A126565 A126566 * A126568 A126569 A126570

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Dec 28 2006

EXTENSIONS

More terms from Robert G. Wilson v, Aug 07 2007

STATUS

approved

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Last modified December 13 19:20 EST 2017. Contains 295976 sequences.