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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
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
Sequence in context: A065357 A119665 A121241 * A158388 A162285 A186035
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.)