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A124040 3 center "cycle" matrices as a triangular sequence based on the triangular model: m(n,m,3)={{3, 1, 1}, {1, 3, 1}, {1, 1, 3}} m(n,m,d)=If[ n == m, 3, If[n == m - 1 || n ==m + 1, 1, If[(n == 1 && m == d) || (n == d && m == 1), 1, 0]]]. 0
3, 3, -1, 8, -6, 1, 20, -24, 9, -1, 45, -84, 50, -12, 1, 125, -275, 225, -85, 15, -1, 320, -864, 900, -468, 129, -18, 1, 845, -2639, 3339, -2219, 840, -182, 21, -1, 2205, -7896, 11756, -9528, 4610, -1368, 244, -24, 1, 5780, -23256, 39825, -38121, 22518, -8532, 2079, -315, 27, -1, 15125, -67650, 130975 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Matrices: 1 X 1 {{3}}, 2 X 2 {{3, 1}, {1, 3}}, 3 X 3 {{3, 1,1}, {1, 3, 1}, {1, 1, 3}}, 4 X 4 {{3, 1, 0, 1}, {1, 3, 1, 0}, {0, 1, 3, 1}, {1, 0, 1, 3}}, 5 X 5 {{3, 1, 0, 0, 1}, {1, 3, 1, 0, 0}, {0, 1, 3, 1, 0}, {0, 0, 1, 3, 1}, {1, 0, 0, 1, 3}} Large Root: Table[x /. NSolve[Det[M[d] - x*IdentityMatrix[d]] == 0, x][[d]], {d, 1, 10}] {3., 4., 5., 5., 5., 5., 5., 5., 5., 5.}

LINKS

Table of n, a(n) for n=1..58.

FORMULA

m(n,m,d)=If[ n == m, 3, If[n == m - 1 || n ==m + 1, 1, If[(n == 1 && m == d) || (n == d && m == 1), 1, 0]]]

EXAMPLE

Triangle begins:

{3},

{3, -1},

{8, -6, 1},

{20, -24, 9, -1},

{45, -84, 50, -12, 1},

{125, -275,225, -85, 15, -1}

MATHEMATICA

T[n_, m_, d_] := If[ n == m, 3, If[n == m - 1 || n == m + 1, 1, If[(n == 1 && m == d) || (n == d && m == 1), 1, 0]]] M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}] Table[M[d], {d, 1, 10}] Table[Det[M[d]], {d, 1, 10}] Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}] a = Join[M[1], Table[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x], {d, 1, 10}]] Flatten[a] MatrixForm[a]

CROSSREFS

Sequence in context: A133709 A173651 A330337 * A248976 A160332 A293294

Adjacent sequences:  A124037 A124038 A124039 * A124041 A124042 A124043

KEYWORD

uned,tabl,sign

AUTHOR

Gary W. Adamson and Roger L. Bagula, Nov 04 2006

STATUS

approved

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Last modified March 29 05:39 EDT 2020. Contains 333105 sequences. (Running on oeis4.)