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%I #7 Jun 13 2015 00:51:33
%S 1,4,32,222,1610,11582,83518,601974,4339414,31280470,225485414,
%T 1625410326,11716765478,84460262198,608831511430
%N A sequence derived from a matrix using "0,1,2,3,4,5,6".
%C Recursion multipliers are seen in rightmost coefficients of the matrix characteristic polynomial, with changed signs: x^3 - 7x^2 - 4x + 18. a(n)/a(n-1) tends to 7.2084965573...a root of the polynomial and an eigenvalue of the matrix.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (7,4,-18).
%F Let M = the 3 X 3 matrix [4 5 6 / 2 3 0 / 1 0 0]. a(n) = rightmost term in M^n * [1 0 0]. a(n+3) = 7*a(n+2) + 4*a(n+1) - 18*a(n).
%F G.f.: -x*(3*x-1) / (18*x^3-4*x^2-7*x+1). [_Colin Barker_, Dec 06 2012]
%e a(5) = 1610 since M^5 * [1 0 0] = [11582 5506 1610]
%e a(9) = 4339414 = 7*601974 + 4*83518 - 18*11582 = 7*a(8) + 4*a(7) - 18*a(6).
%K nonn,easy
%O 1,2
%A _Gary W. Adamson_, Oct 10 2004
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