|
Search: id:A122374
|
|
|
| A122374 |
|
Hollow triangular anti-diagonal matrices give a triangular array: 1, 1 - x, -1 - x + x^2, -1 + x + 2 x^2 - x^3, 1 - x - 4 x^2 - x^3 + x^4, 1 - 3 x - 3 x^2 + 4 x^3 + 2 x^4 - x^5. |
|
+0
1
|
|
| 1, 1, -1, -1, -1, 1, -1, 1, 2, -1, 1, -1, -4, -1, 1, 1, -3, -3, 4, 2, -1, -1, 3, 7, -2, -7, -1, 1, -1, 5, 4, -11, -5, 7, 2, -1, 1, -5, -10, 9, 18, -3, -10, -1, 1, 1, -7, -5, 22, 9, -24, -7, 10, 2, -1, -1, 7, 13, -20, -34, 18, 34, -4, -13, -1, 1, -1, 9, 6, -37, -14, 58, 16, -42, -9, 13, 2, -1, 1, -9, -16, 35, 55, -50, -80, 30, 55, -5, -16, -1, 1
(list; graph; listen)
|
|
|
OFFSET
|
1,9
|
|
|
COMMENT
|
Hollow matrices ( only hollow at 4 X 4 and above): 2 X 2 {{0, 1}, {1, 1}} 3 X 3 {{0, 0, 1}, {0, 1, 1}, {1, 1, 1}} 4 X 4 {{0, 0, 0, 1}, {0, 0, 1, 1}, {0, 1, 0, 1}, {1, 1, 1, 1}} 5 X 5 {{0, 0, 0, 0, 1}, {0, 0, 0, 1, 1}, {0, 0, 1, 0, 1}, {0, 1, 0, 0, 1}, {1, 1, 1, 1, 1}} 6 X 6 {{0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 1}, { 0, 0, 0, 1, 0, 1}, {0, 0, 1, 0, 0, 1}, { 0, 1, 0, 0, 0, 1}, {1, 1, 1, 1, 1, 1}},
|
|
FORMULA
|
A(i,j)->p(n,x) p(n,x)-t(n,m)
|
|
EXAMPLE
|
Triangular array:
{1},
{1, -1},
{-1, -1, 1},
{-1, 1, 2, -1},
{1, -1, -4, -1, 1},
{1, -3, -3,4, 2, -1},
{-1, 3, 7, -2, -7, -1, 1},
{-1, 5, 4, -11, -5,7, 2, -1},
{1, -5, -10, 9, 18, -3, -10, -1, 1},
{1, -7, -5, 22, 9, -24, -7,10, 2, -1}
|
|
MATHEMATICA
|
An[d_] := Table[If[n + m - 1 == d, 1, If[n - d == 0, 1, If[m - d == 0, 1, 0]]], {n, 1, d}, {m, 1, d}]; Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d, 1, 20}]]; Flatten[%]
|
|
CROSSREFS
|
Sequence in context: A054772 A085384 A067856 this_sequence A010121 A139320 A118106
Adjacent sequences: A122371 A122372 A122373 this_sequence A122375 A122376 A122377
|
|
KEYWORD
|
uned,sign
|
|
AUTHOR
|
Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Oct 19 2006
|
|
|
Search completed in 0.002 seconds
|
