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 A122188 Triangle read by rows, formed from the coefficients of characteristic polynomials of the following sequence of matrices: 2 X 2 {{0, 1}, {1, 1}}, 3 X 3 {{0, 1, 0}, {0, 0, 1}, {1, 1, 1}}, 4 X 4 {{0, 1,0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 1, 1, 1}}, 5 X 5 {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 1, 1, 1, 1}}, ... 2
 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row sums are {1, 0, -1, 2, -3, 4, -5, 6, -7, 8, -9}. LINKS Table of n, a(n) for n=1..104. FORMULA B(x, n) = If[n > 1, (-1)^n*(x^n - Sum[x^m, {m, 0, n - 1}])] EXAMPLE Triangular array: {1}, {1, -1}, {-1, -1, 1}, {1, 1, 1, -1}, {-1, -1, -1, -1, 1}, {1, 1, 1,1, 1, -1}, {-1, -1, -1, -1, -1, -1,1}, {1, 1, 1, 1, 1, 1, 1, -1}, {-1, -1, -1, -1, -1, -1, -1, -1, 1} MATHEMATICA An[d_] := Table[If[n == d, 1, If[m == n + 1, 1, 0]], {n, 1, d}, {m, 1, d}]; Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d, 1, 20}]]; Flatten[%] Clear[B, x, n] B[x, 0] = 1; B[x, 1] = -x + 1; B[x_, n_] := B[x, n] = If[n > 1, (-1)^n*(x^n - Sum[x^m, {m, 0, n - 1}])]; Table[ExpandAll[B[x, n]], {n, 0, 10}]; a = Table[CoefficientList[B[x, n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[B[x, n], x]], {n, 0, 10}] CROSSREFS Cf. A000073, A000045. Sequence in context: A065357 A119665 A121241 * A158388 A162285 A186035 Adjacent sequences: A122185 A122186 A122187 * A122189 A122190 A122191 KEYWORD tabl,sign AUTHOR Gary W. Adamson and Roger L. Bagula, Oct 18 2006, Mar 18 2008 EXTENSIONS Edited by N. J. A. Sloane, Apr 14 2008 STATUS approved

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Last modified March 4 14:06 EST 2024. Contains 370532 sequences. (Running on oeis4.)