The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A158285 A triangle of coefficients of matrix polynomials:M(d)=If[ m == n, -1, 1] (odd orthogonality) 0
 1, -1, -1, 0, 2, 1, 4, 0, -3, -1, -16, -16, 0, 4, 1, 48, 80, 40, 0, -5, -1, -128, -288, -240, -80, 0, 6, 1, 320, 896, 1008, 560, 140, 0, -7, -1, -768, -2560, -3584, -2688, -1120, -224, 0, 8, 1, 1792, 6912, 11520, 10752, 6048, 2016, 336, 0, -9, -1, -4096, -17920 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, -2, 3, 0, -27, 162, -729, 2916, -10935, 39366, -137781,...}. These matrices are an all ones matrix with central diagonal negative. These matrices have the odd orthogonality property of: M(n).M(n)-M(n)-(-5+n)*Ones(n)=6*IdentityMatirix[n]; Table[T[n, m, d], {n, 1, d}, {m, 1, d}].Table[T[n, m, d], {n, 1, d}, {m, 1, d}] - Table[T[n, m, d], {n, 1, d}, {m, 1, d}] - (-5 + d)*Table[1, {n, d}, {m, d}] Matrix example: M(3)={{-1, 1, 1}, {1, -1, 1}, {1, 1, -1}} LINKS FORMULA M(d)=If[ m == n, -1, 1]; out_(n,m)=coefficients(characteristicpolynomial(M(n),x),x) EXAMPLE {1}, {-1, -1}, {0, 2, 1}, {4, 0, -3, -1}, {-16, -16, 0, 4, 1}, {48, 80, 40, 0, -5, -1}, {-128, -288, -240, -80, 0, 6, 1}, {320, 896, 1008, 560, 140, 0, -7, -1}, {-768, -2560, -3584, -2688, -1120, -224, 0, 8, 1}, {1792, 6912, 11520, 10752, 6048, 2016, 336, 0, -9, -1}, {-4096, -17920, -34560, -38400, -26880, -12096, -3360, -480, 0, 10, 1} MATHEMATICA Clear[M, T, d, a, x, a0]; T[n_, m_, d_] := If[ m == n, -1, 1]; M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}]; a0 = 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: A048614 A001442 A226952 * A277994 A334112 A286238 Adjacent sequences:  A158282 A158283 A158284 * A158286 A158287 A158288 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Mar 15 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 1 08:39 EDT 2020. Contains 337442 sequences. (Running on oeis4.)