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A123190
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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 ]].
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1
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1, 0, 6, -6, 120, -504, 5268, -33960, 286872, -2089656, 16524528, -124872576, 967652400, -7394858496, 56948789280, -436704535776, 3356724764544, -25767744878592, 197948016193344, -1520029557845376, 11674792161026688, -89658816678161280, 688598927703310080
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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
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MAPLE
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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);
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MATHEMATICA
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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}]
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PROG
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(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
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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