|
|
A122773
|
|
Triangular array, see Mathematica code.
|
|
1
|
|
|
2, 1, -1, -4, 2, 1, 4, -4, 2, -1, -16, 24, -16, 4, 1, 16, -32, 28, -12, 3, -1, -64, 160, -176, 104, -36, 6, 1, 64, -192, 256, -192, 88, -24, 4, -1, -256, 896, -1408, 1280, -736, 272, -64, 8, 1, 256, -1024, 1856, -1984, 1376, -640, 200, -40, 5, -1, -1024, 4608, -9472, 11648, -9472, 5312, -2080, 560, -100, 10, 1, 1024
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
REFERENCES
|
Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.
|
|
LINKS
|
|
|
EXAMPLE
|
Triangular array:
{2},
{1, -1},
{-4, 2, 1},
{4, -4, 2, -1},
{-16, 24, -16, 4, 1},
{16, -32, 28, -12, 3, -1},
{-64, 160, -176, 104, -36, 6, 1},
{64, -192, 256, -192, 88, -24, 4, -1}
|
|
MATHEMATICA
|
An[d_] := Table[If[n == d, 1, If[m == n + 1, 1, 0]], {n, 1, d}, {m, 1, d}];
Join[{{2}}, Table[CoefficientList[CharacteristicPolynomial[2*IdentityMatrix[d] + MatrixPower[An[d], -1], x], x], {d, 1, 20}]]
Flatten[%]
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
_Gary W. Adamson_ and _Roger L. Bagula_, Oct 20 2006
|
|
STATUS
|
approved
|
|
|
|