A155706 A(n,m,k)=If[m less than n, 1, -1]; p(x,k)=(-1)^n*CharacteristicPolynomial[A[n,m,k],x]; t(n,m)=coefficients(p(x,n)+x^n*p(1/x,n)), triangle read by rows.

1, 2, 2, 3, 4, 3, 5, 9, 9, 5, 9, 20, 24, 20, 9, 17, 45, 60, 60, 45, 17, 33, 102, 150, 160, 150, 102, 33, 65, 231, 378, 420, 420, 378, 231, 65, 129, 520, 952, 1120, 1120, 1120, 952, 520, 129, 257, 1161, 2376, 3024, 3024, 3024, 3024, 2376, 1161, 257, 513, 2570, 5850

Offset

0,2

Links

Table of n, a(n) for n=0..57.

Example

{1},
{2, 2},
{3, 4, 3},
{5, 9, 9, 5},
{9, 20, 24, 20, 9},
{17, 45, 60, 60, 45, 17},
{33, 102, 150, 160, 150, 102, 33},
{65, 231, 378, 420, 420, 378, 231, 65},
{129, 520, 952, 1120, 1120, 1120, 952, 520, 129},
{257, 1161, 2376, 3024, 3024, 3024, 3024, 2376, 1161, 257},
{513, 2570, 5850, 8160, 8400, 8064, 8400, 8160, 5850, 2570, 513}

Mathematica

A[k_] := Table[If[m < n, 1, -1], {m, k}, {n, k}]; a = Join[{{1}}, Table[(-1)^n*CoefficientList[CharacteristicPolynomial[A[n], x], x] + Reverse[(-1)^n* CoefficientList[CharacteristicPolynomial[A[n], x],  x]], {n, 1, 10}]];
Flatten[a]

Crossrefs

Sequence in context: A037254 A316939 A259478 * A317533 A360999 A343299

Adjacent sequences: A155703 A155704 A155705 * A155707 A155708 A155709

Keyword

nonn,tabl,uned

Author

Roger L. Bagula and Gary W. Adamson, Jan 25 2009

Status

approved