A144474 A triangle sequence of determinants: a(n)=If[Mod[n, 2] == 0, 1, If[Mod[n, 2] == 1, -1, 0]]; b(n,m)=If[m < n && Mod[n, 3] == 0, 0, If[m < n && Mod[n, 3] == 1, 0, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 0, 1, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 1, -1, If[m == n, -1, 0]]]]]; M={{a(m), b(n, m)}, {a(n), b(n, n)}}; t(n,m)=Det[M].

-1, -2, 0, -1, 1, -1, -1, 1, -1, 1, -2, 0, -2, 0, -2, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -2, 0, -2, 0, -2, 0, -2, 0, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1

Offset

1,2

Comments

Row sums are:{-1, -2, -1, 0, -6, 0, -1, -8, -1, 0}.

Links

Table of n, a(n) for n=1..55.

Formula

a(n)=If[Mod[n, 2] == 0, 1, If[Mod[n, 2] == 1, -1, 0]]; b(n,m)=If[m < n && Mod[n, 3] == 0, 0, If[m < n && Mod[n, 3] == 1, 0, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 0, 1, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 1, -1, If[m == n, -1, 0]]]]]; M={{a(m), b(n, m)}, {a(n), b(n, n)}}; t(n,m)=Det[M].

Example

{-1},
{-2, 0},
{-1, 1, -1},
{-1, 1, -1, 1},
{-2, 0, -2, 0, -2},
{-1, 1, -1, 1, -1, 1},
{-1, 1, -1, 1, -1, 1, -1},
{-2, 0, -2, 0, -2, 0, -2, 0},
{-1, 1, -1, 1, -1, 1, -1, 1, -1},
{-1, 1, -1, 1, -1, 1, -1, 1, -1, 1}

Mathematica

Clear[a, b, t, n, m] a[n_] := If[Mod[n, 2] == 0, 1, If[Mod[n, 2] == 1, -1, 0]]; b[n, m_] := If[m < n && Mod[n, 3] == 0, 0, If[m < n && Mod[n, 3] == 1, 0, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 0, 1, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 1, -1, If[m == n, -1, 0]]]]]; M = {{a[m], b[n, m]}, {a[n], b[n, n]}}; t[n_, m_] := Det[M]; Table[Table[t[n, m], {m, 0, n - 1}], {n, 1, 10}]; Flatten[%]

Crossrefs

Sequence in context: A327406 A336865 A262257 * A298602 A203949 A070200

Adjacent sequences: A144471 A144472 A144473 * A144475 A144476 A144477

Keyword

sign,uned

Author

Roger L. Bagula and Gary W. Adamson, Oct 10 2008

Status

approved