A124028 Center antidiagonal four in a tri-antidiagonal n-th Matrix generated triangular sequence: first element as 4==m[1,1,1].

4, 4, -1, -15, 2, 1, -56, 18, 4, -1, 209, -34, -33, 2, 1, 780, -259, -128, 36, 4, -1, -2911, 484, 738, -70, -51, 2, 1, -10864, 3620, 2824, -842, -200, 54, 4, -1, 40545, -6756, -14178, 1614, 1591, -106, -69, 2, 1, 151316, -50437, -53888, 16564, 6164, -1749, -272, 72, 4, -1, -564719, 94118, 251811, -31514, -39629

Offset

1,1

Comments

These matrices and triangular sequences are machine generated: all we have done is invent the matrix form "tri-antidiagonal matrices" and get a way to compute it. Matrices: {{4}}, {{-1, 4}, {4, -1}}, {{0, -1, 4}, {-1, 4, -1}, {4, -1, 0}}, {{0, 0, -1, 4}, {0, -1, 4, -1}, {-1, 4, -1, 0}, {4, -1, 0, 0}}, {{0, 0, 0, -1, 4}, {0, 0, -1, 4, -1}, {0, -1, 4, -1, 0}, {-1, 4, -1, 0, 0}, {4, -1, 0, 0,0}}

Links

Table of n, a(n) for n=1..60.

Formula

m(n,m,d)=If[n + m - 1 == d, 4, If[n + m == d, -1, If[n + m - 2 == d, -1, 0]]]

Example

Triangular sequence:
{4},
{4, -1},
{-15, 2, 1},
{-56, 18, 4, -1},
{209, -34, -33, 2, 1},
{780, -259, -128, 36, 4, -1},
{-2911, 484, 738, -70, -51, 2, 1},
{-10864, 3620, 2824, -842, -200, 54, 4, -1},
{40545, -6756, -14178, 1614, 1591, -106, -69, 2, 1}

Mathematica

An[d_] := Table[If[n + m - 1 == d, 4, If[n + m == d, -1, If[n + m - 2 == d, -1, 0]]], {n, 1, d}, {m, 1, d}]; Join[An[1], Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d, 1, 20}]]; Flatten[%]

Crossrefs

Sequence in context: A140313 A102323 A145902 * A123966 A371898 A079507

Adjacent sequences: A124025 A124026 A124027 * A124029 A124030 A124031

Keyword

uned,sign

Author

Roger L. Bagula and Gary W. Adamson, Nov 01 2006

Status

approved