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 A124032 Triangle read by rows: T(n,k) is the coefficient of x^k in the polynomial p(n,x) defined by p(0,x)=1, p(1,x)=-1-x, p(n,x)=((-1)^(n-1)-x)*p(n-1,x)-p(n-2,x) for n>=2 (0<=k<=n). 1
 1, -1, -1, 0, 2, 1, 1, 3, -1, -1, -1, -6, -3, 2, 1, -2, -8, 4, 6, -1, -1, 3, 16, 7, -12, -6, 2, 1, 5, 21, -13, -25, 7, 9, -1, -1, -8, -42, -15, 50, 24, -18, -9, 2, 1, -13, -55, 40, 90, -33, -51, 10, 12, -1, -1, 21, 110, 30, -180, -81, 102, 50, -24, -12, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Joanne Dombrowski, Tridiagonal matrix representations of cyclic selfadjoint operators, Pacific J. Math. 114, no. 2 (1984), 325-334. EXAMPLE Triangle begins: {1}, {-1, -1}, {0, 2, 1}, {1,3, -1, -1}, {-1, -6, -3, 2, 1}, {-2, -8, 4, 6, -1, -1}, {3, 16, 7, -12, -6, 2, 1}, {5, 21, -13, -25, 7, 9, -1, -1}, {-8, -42, -15, 50, 24, -18, -9, 2, 1}, {-13, -55, 40, 90, -33, -51, 10, 12, -1, -1}, {21,110, 30, -180, -81, 102, 50, -24, -12, 2, 1}} MAPLE p[0]:=1: p[1]:=-1-x: for n from 2 to 12 do p[n]:=sort(expand(((-1)^(n-1)-x)*p[n-1]-p[n-2])) od: T:=(n, k)->coeff(p[n], x, k): for n from 0 to 12 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form MATHEMATICA b[k_] = (-1)^k; a[k_] = -1; p[0, x] = 1; p[1, x] = (x - b[1])/a[1]; p[k_, x_] :=p[k, x] = ((x - b[k - 1])*p[k - 1, x] - a[k - 2] *p[k - 2, x])/a[k - 1]; w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w] CROSSREFS Sequence in context: A195825 A098824 A181651 * A254046 A137457 A275699 Adjacent sequences:  A124029 A124030 A124031 * A124033 A124034 A124035 KEYWORD sign,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, Nov 01 2006 EXTENSIONS Edited by N. J. A. Sloane, Dec 02 2006 STATUS approved

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Last modified May 10 03:11 EDT 2021. Contains 343747 sequences. (Running on oeis4.)