A144473 - OEIS

A144473

A triangle sequence of determinants: a(n)=If[Mod[n, 3] == 0, 1, If[Mod[n, 3] == 1, -1, If[Mod[n, 3] == 2, 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, -1, 1, -1, 1, 0, -1, 1, 0, -1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, -1, 1, 0, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, -1

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OFFSET

1,1

COMMENTS

Row sums are:{-1, 0, 0, -1, 0, 0, -1, 0, 0, -1}.

LINKS

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

FORMULA

a(n)=If[Mod[n, 3] == 0, 1, If[Mod[n, 3] == 1, -1, If[Mod[n, 3] == 2, 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},

{-1, 1},

{-1, 1, 0},

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

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

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

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

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

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

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

MATHEMATICA

Clear[a, b, t, n, m] a[n_] := If[Mod[n, 3] == 0, 1, If[Mod[n, 3] == 1, -1, If[Mod[n, 3] == 2, 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: A071038 A131522 A221641 * A011750 A340375 A010055

Adjacent sequences: A144470 A144471 A144472 * A144474 A144475 A144476

KEYWORD

sign,uned

AUTHOR

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

STATUS

approved