A158391 Triangle of characteristic polynomials, see Mathematica code.

1, 1, -1, 4, -6, 1, 36, -62, 20, -1, 576, -1064, 440, -50, 1, 14400, -27752, 13092, -2068, 105, -1, 518400, -1027872, 526240, -99568, 7476, -196, 1, 25401600, -51402528, 27827104, -5903560, 552368, -22488, 336, -1, 1625702400, -3340564992, 1883221312, -432454176, 46632432, -2444400, 59004, -540, 1

Offset

0,4

Comments

Example matrix: M(3)={{14, 5, 1}, {5, 5, 1}, {1, 1, 1}}

Links

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

Example

Triangle begins:
  {1},
  {1, -1},
  {4, -6, 1},
  {36, -62, 20, -1},
  {576, -1064, 440, -50, 1},
  {14400, -27752, 13092, -2068, 105, -1},
  {518400, -1027872, 526240, -99568, 7476, -196, 1},
  {25401600, -51402528, 27827104, -5903560, 552368, -22488, 336, -1},
  {1625702400, -3340564992, 1883221312, -432454176, 46632432, -2444400, 59004, -540, 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: A333668 A193293 A258220 * A379778 A016491 A347052

Adjacent sequences: A158388 A158389 A158390 * A158392 A158393 A158394

Keyword

sign,tabl,less

Author

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

Status

approved