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 A144475 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[m, 3] == 0, 0, If[m < n && Mod[m, 3] == 1, 0, If[m < n && Mod[m, 3] == 2 && Mod[n, 2] == 0, 1, If[m < n && Mod[m, 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]. 0
 -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 0, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 0, -1, 1, 0, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row sums are:{-1, 0, 1, 0, 0, -2, -3, 0, 3, 2}. It took me a while to get the projection right. The example three matrices are: Table[M /. n -> 4, {m, 1, 3}] M1={{-1, 0}, {-1, -1}}; M2={{0, 1}, {-1, -1}}; M3={{1, 0}, {-1, -1}}; Characteristic polynomials: Table[CharacteristicPolynomial[M /. n -> 4, x], {m, 1, 3}]; {1 + 2 x + x^2, 1 + x + x^2, -1 + x^2}. LINKS 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[m, 3] == 0, 0, If[m < n && Mod[m, 3] == 1, 0, If[m < n && Mod[m, 3] == 2 && Mod[n, 2] == 0, 1, If[m < n && Mod[m, 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, 1}, {-1, 1, 1, -1}, {-1, 1, 0, -1, 1}, {-1, 1, -1, -1, 1, -1}, {-1, 1, -1, -1, 1, -1, -1}, {-1, 1, 0, -1, 1, 0, -1, 1}, {-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, 3] == 0, 1, If[Mod[n, 3] == 1, -1, If[Mod[n, 3] == 2, 0]]]; b[n_, m_] := If[m < n && Mod[m, 3] == 0, 0, If[m < n && Mod[m, 3] == 1, 0, If[m < n && Mod[m, 3] == 2 && Mod[n, 2] == 0, 1, If[m < n && Mod[m, 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: A108358 A267959 A144384 * A011758 A015088 A015166 Adjacent sequences:  A144472 A144473 A144474 * A144476 A144477 A144478 KEYWORD sign,uned AUTHOR Roger L. Bagula and Gary W. Adamson, Oct 10 2008 STATUS approved

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Last modified September 20 14:44 EDT 2021. Contains 347586 sequences. (Running on oeis4.)