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 A100296 Sequence generated from a symmetric matrix. 1

%I

%S 1,6,25,111,488,2149,9461,41654,183389,807403,3554736,15650361,

%T 68903513,303360038,1335596817,5880203831,25888648920,113979406525,

%U 501814720109,2209329044566,9726966211957,42824708216851,188543436246752,830096195208753,3654646945111665

%N Sequence generated from a symmetric matrix.

%C A100295 is generated from M^n * [1 0 0]. a(n)/a(n-1) tends to 4.4026788295...a root of the characteristic polynomial of M, x^3 - 4x^2 - 2x + 1 and an eigenvalue of M.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (4,2,-1).

%F a(n) = rightmost term in M^n * [1 1 1]. a(n) = 4*a(n-1) + 2*a(n-2) - a(n-3).

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

%e a(5) = 488 since M^5 * [1 1 1] = [2149 1263 488]. 2149 = a(6).

%e a(8) = 4*a(7) + 2*a(6) - a(5) =41654 = 4*9461 + 2*2149 - 488.

%Y Cf. A100295.

%K nonn,easy

%O 1,2

%A _Gary W. Adamson_, Nov 11 2004

%E More terms from _Colin Barker_, May 25 2013

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Last modified October 22 22:35 EDT 2021. Contains 348180 sequences. (Running on oeis4.)