A158390 Triangle of characteristic polynomials, see Mathematica code.

1, 1, -1, -4, -1, 1, -36, 9, 5, -1, 576, 64, -61, -5, 1, 14400, -1600, -1045, 105, 14, -1, -518400, -32400, 29088, 1593, -385, -14, 1, -25401600, 1587600, 1079200, -63481, -11521, 579, 30, -1, 1625702400, 65028096, -55637056, -2062912, 523001, 16045, -1563, -30, 1

Offset

0,4

Comments

Example matrix: M(3)= {{1, 2, 3}, {2, 4, 0}, {3, 0, 0}}.

Links

Table of n, a(n) for n=0..44.

Example

Triangle begins:
  {1},
  {1, -1},
  {-4, -1, 1},
  {-36, 9, 5, -1},
  {576, 64, -61, -5, 1},
  {14400, -1600, -1045, 105, 14, -1},
  {-518400, -32400, 29088, 1593, -385, -14, 1},
  {-25401600, 1587600, 1079200, -63481, -11521, 579, 30, -1},
  {1625702400, 65028096, -55637056, -2062912, 523001, 16045, -1563, -30, 1}

Mathematica

M[d_] :=Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]]*Transpose[Reverse[Table[If[ m <= n, m, 0], {n, 1, d}, {m, 1, d}]]];
a = Table[CharacteristicPolynomial[M[d], x], {d, 1, 10}];
Join[{1}, Flatten[CoefficientList[a, x]]]

Crossrefs

Sequence in context: A174412 A177939 A209196 * A386677 A228836 A176419

Adjacent sequences: A158387 A158388 A158389 * A158391 A158392 A158393

Keyword

sign,tabl,less

Author

Roger L. Bagula and Gary W. Adamson, Mar 17 2009

Status

approved