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A119516
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So(5)-like pattern matrix of alternating sign 5 X 5 Matrix Markov with low ratio and characteristic polynomial: 5*x^4+10*x^2+1.
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0
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0, 1, 9, -3, -83, 25, 785, -235, -7435, 2225, 70425, -21075, -667075, 199625, 6318625, -1890875, -59850875, 17910625, 566915625, -169651875, -5369901875, 1606965625, 50864440625, -15221396875, -481794896875, 144179140625, 4563626765625, -1365684421875, -43227293171875
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| M = Table[If[n == m, 0, If[n > m, -(-1)^(n + m), (-1)^(n + m)]], {n, 1, 5}, {m, 1, 5}]; w[1] = {0, 1, 1, 2, 3}; w[n_] := w[n] = M.w[n - 1] a[n]=w[n][[1]]
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EXAMPLE
| Diagonals alternate in sign, main diagonal zero:
{{0, -1, 1, -1, 1},
{1, 0, -1, 1, -1},
{-1, 1, 0, -1, 1},
{1, -1, 1,0, -1},
{-1, 1, -1, 1, 0}}
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MATHEMATICA
| M = Table[If[n == m, 0, If[n > m, -(-1)^(n + m), (-1)^(n + m)]], {n, 1, 5}, {m, 1, 5}]; w[1] = {0, 1, 1, 2, 3}; w[n_] := w[n] = M.w[n - 1] a = Table[w[n][[1]], {n, 1, 30}]
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CROSSREFS
| Sequence in context: A040077 A195312 A038293 * A193109 A197828 A116393
Adjacent sequences: A119513 A119514 A119515 * A119517 A119518 A119519
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KEYWORD
| sign,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com)), Jul 27 2006
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