|
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Row sums are: {1, 0, -1, 2, -3, 4, -5, 6, -7, 8, -9}
|
|
|
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: A064179 A065357 A121241 * A000012 A158388 A162285
Adjacent sequences: A122185 A122186 A122187 * A122189 A122190 A122191
|
|
|
KEYWORD
| tabl,sign
|
|
|
AUTHOR
| Gary Adamson and Roger Bagula (qntmpkt(AT)yahoo.com), Oct 18 2006, Mar 18 2008
|
|
|
EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 14 2008
|
| |
|
|
