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 A120391 Expansion of -x*(1+x-x^2+x^3+4*x^4) / ( (x^3-2*x^2-x+1)*(x^3+2*x^2-x-1) ). 0
 0, 1, 1, 4, 6, 18, 24, 67, 85, 231, 287, 771, 949, 2536, 3108, 8285, 10133, 26980, 32966, 87726, 107140, 285035, 348037, 925799, 1130311, 3006511, 3670473, 9762796, 11918536, 31700713, 38700153, 102933300, 125660022, 334225018, 408017728 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Top element of the vector obtained by multiplying the n-th power of the 6 X 6 matrix [[0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0]] by the column vector [0, 1, 1, 2, 3, 5]. LINKS Index entries for linear recurrences with constant coefficients, signature (0,5,0,-6,0,1). MATHEMATICA M = {{0, 1, 0, 0, 0, 0}, {1, 0, 1, 0, 0, 0}, {0, 1, 0, 1, 0, 0}, {0, 0, 1, 0, 1, 0}, {0, 0, 0, 1, 0, 1}, {0, 0, 0, 0, 1, 0}} v[1] = {0, 1, 1, 2, 3, 5} v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}] Det[M - x*IdentityMatrix[6]] Factor[%] aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[6]] == 0, x][[n]], {n, 1, 6}] Abs[aaa] a1 = Table[N[a[[n]]/a[[n - 1]]], {n, 7, 50}] CoefficientList[Series[-x(1+x-x^2+x^3+4x^4)/((x^3-2x^2-x+1)(x^3+ 2x^2- x-1)), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 5, 0, -6, 0, 1}, {0, 1, 1, 4, 6, 18}, 40] (* Harvey P. Dale, Feb 05 2012 *) CROSSREFS Sequence in context: A109310 A219190 A337617 * A064217 A026623 A026689 Adjacent sequences:  A120388 A120389 A120390 * A120392 A120393 A120394 KEYWORD nonn AUTHOR Roger L. Bagula and Gary W. Adamson), Jun 30 2006 STATUS approved

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Last modified May 16 14:31 EDT 2022. Contains 353704 sequences. (Running on oeis4.)