A136450 Matrix based on counter variant Hankel matrix: (smaller at central antidiagonal) h(i,j) = If[i + j - 1 > n, 0, n + 1 - (i + j - 1) Characteristic polynomials as a triangle of coefficients.

1, 1, -1, -1, -2, 1, -1, 2, 4, -1, 1, 2, -7, -6, 1, 1, -2, -10, 12, 9, -1, -1, -2, 13, 18, -26, -12, 1, -1, 2, 16, -24, -52, 40, 16, -1, 1, 2, -19, -30, 87, 86, -70, -20, 1, 1, -2, -22, 36, 131, -150, -190, 100, 25, -1, -1, -2, 25, 42, -184, -232, 403, 294, -155, -30, 1

Offset

1,5

Comments

These polynomials grow slower than their Hankel counterparts.

Row sums are {1, 0, -2, 4, -9, 9, -9, -4, 38, -72, 161}.

Links

Table of n, a(n) for n=1..66.

Formula

h(i,j)=If[i + j - 1 > n, 0, n + 1 - (i + j - 1): i,j<=n.

Example

{1},
{1, -1},
{-1, -2, 1},
{-1, 2, 4, -1},
{1, 2, -7, -6, 1},
{1, -2, -10,12, 9, -1},
{-1, -2, 13, 18, -26, -12, 1},
{-1, 2, 16, -24, -52, 40, 16, -1},
{1, 2, -19, -30, 87, 86, -70, -20, 1},
{1, -2, -22, 36,131, -150, -190, 100, 25, -1},
{-1, -2, 25, 42, -184, -232,403, 294, -155, -30, 1}

Mathematica

H[n_] := Table[Table[If[i + j - 1 > n, 0, n + 1 - (i + j - 1)], {i, 1, n}], {j, 1, n}]; a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[H[n], x], x], {n, 1, 10}]]; Flatten[a]

Crossrefs

Sequence in context: A110971 A136788 A334622 * A355011 A131054 A267998

Adjacent sequences: A136447 A136448 A136449 * A136451 A136452 A136453

Keyword

uned,tabl,sign

Author

Roger L. Bagula, Mar 19 2008

Status

approved