|
Search: id:A145661
|
|
|
| A145661 |
|
A signed version of A119258 from a matrix which is related to A122188 (Bonacci matrices and polynomials) by matrix powers. That the result is related to Pascal's triangle seems amazing. |
|
+0
2
|
|
| 1, 1, -1, 1, -3, 1, 1, -5, 7, -1, 1, -7, 17, -15, 1, 1, -9, 31, -49, 31, -1, 1, -11, 49, -111, 129, -63, 1, 1, -13, 71, -209, 351, -321, 127, -1, 1, -15, 97, -351, 769, -1023, 769, -255, 1, 1, -17, 127, -545, 1471, -2561, 2815, -1793, 511, -1, 1, -19, 161, -799, 2561
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Row sums of signed version of A119258:
{1, 0, -1, 2, -3, 4, -5, 6, -7, 8, -9,...}.
Example matrix:
M(3)={{1, 1, 1},
{1, 2, 2},
{2, 3, 4}}.
|
|
FORMULA
|
out_(n,m)=coefficients(characteristicpolynomial(m(d),x),x).
|
|
EXAMPLE
|
{1, -1},
{1, -3, 1},
{1, -5, 7, -1},
{1, -7, 17, -15, 1},
{1, -9, 31, -49, 31, -1},
{1, -11, 49, -111, 129, -63, 1},
{1, -13, 71, -209, 351, -321, 127, -1},
{1, -15, 97, -351, 769, -1023, 769, -255, 1},
{1, -17, 127, -545, 1471, -2561, 2815, -1793, 511, -1},
{1, -19, 161, -799, 2561, -5503, 7937, -7423, 4097, -1023, 1}
|
|
MATHEMATICA
|
Clear[M, T, d, a, x, a0];
T[n_, m_, d_] := If[ m == n + 1, 1, If[n == d, 1, 0]];
M[d_] := MatrixPower[Table[T[n, m, d], {n, 1, d}, {m, 1, d}], d];
Table[M[d], {d, 1, 10}];
Table[Det[M[d]], {d, 1, 10}];
Table[CharacteristicPolynomial[M[d], x], {d, 1, 10}];
a = Join[{{1}}, Table[CoefficientList[Expand[CharacteristicPolynomial[M[n], x]], x], {n, 1, 10}]];
Flatten[a]
Join[{1}, Table[Apply[ Plus, CoefficientList[Expand[CharacteristicPolynomial[M[n], x]], x]], {n, 1, 10}]];
|
|
CROSSREFS
|
Sequence in context: A114172 A121522 A080842 this_sequence A119258 A099608 A047969
Adjacent sequences: A145658 A145659 A145660 this_sequence A145662 A145663 A145664
|
|
KEYWORD
|
tabf,uned,sign
|
|
AUTHOR
|
Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Mar 16 2009.
|
|
|
Search completed in 0.002 seconds
|
