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A123190 Sum of the entries of the first row of the matrix M^n, where M is the 4 X 4 matrix [[ -1, 3, -3, 1 ], [ 3, -6, 3, 0 ], [ -3, 0, 3, 0 ], [ 1, 4, 1, 0 ]]. 1

%I

%S 1,0,6,-6,120,-504,5268,-33960,286872,-2089656,16524528,-124872576,

%T 967652400,-7394858496,56948789280,-436704535776,3356724764544,

%U -25767744878592,197948016193344,-1520029557845376,11674792161026688,-89658816678161280,688598927703310080

%N Sum of the entries of the first row of the matrix M^n, where M is the 4 X 4 matrix [[ -1, 3, -3, 1 ], [ 3, -6, 3, 0 ], [ -3, 0, 3, 0 ], [ 1, 4, 1, 0 ]].

%H Colin Barker, <a href="/A123190/b123190.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-4,34,30,-108).

%F G.f.: (1 + 4*x - 28*x^2 - 12*x^3) / (1 + 4*x - 34*x^2 - 30*x^3 + 108*x^4). - _Colin Barker_, Dec 13 2012

%F a(n) = -4*a(n-1) + 34*a(n-2) + 30*a(n-3) - 108*a(n-4) for n>3. - _Colin Barker_, Mar 03 2017

%p with(linalg): M[1]:=matrix(4,4,[ -1,3,-3,1,3,-6,3,0,-3,0,3,0,1,4,1,0]): for n from 2 to 22 do M[n]:=multiply(M[n-1],M[1]) od: 1,seq(add(M[k][1,j],j=1..4),k=1..22);

%t M = {{ -1, 3, -3, 1 }, { 3, -6, 3, 0 }, {-3, 0, 3, 0 }, { 1, 4, 1, 0 }}; v[1] = {1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1] a1 = Table[v[n][[1]], {n, 1, 25}]

%o (PARI) Vec((1 + 4*x - 28*x^2 - 12*x^3) / (1 + 4*x - 34*x^2 - 30*x^3 + 108*x^4) + O(x^30)) \\ _Colin Barker_, Mar 03 2017

%K sign,easy

%O 0,3

%A _Roger L. Bagula_, Oct 03 2006

%E Edited by _N. J. A. Sloane_, Oct 26 2006

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Last modified July 25 20:28 EDT 2021. Contains 346291 sequences. (Running on oeis4.)