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A147833
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A vector matrix Markov based on the simplex point matrix for the {3.4,5} triangle:Points{x,y}:{0,0},{0,3},{0,4}; M0={{1,0,0} {1,0,3}, {1,4,0}}; 3^2+4^2=5^2; with characteristic polynomial: 12 + 4 x + x^2 - x^3
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1, 0, 0, 12, 12, 60, 252, 636, 2364, 7932, 25020, 85116, 280380, 921084, 3063996, 10112892, 33421884, 110641404, 365683644, 1209311868, 3999743292, 13225194492, 43735910076, 144633607548, 478279581756, 1581644932860
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| This area one simplex matrix when rotated {{1,0,0} {1,0,1}, {1,1,0}} Gives: {{0,1,0}, {0,0,1}, {1,1,1}} which is associated with the tribonacci or Rauzy tile. That open the way for the 3,4,5 triangle being: {{1,0,0} {1,0,3}, {1,4,0}} 3^2+4^2=5^2 The Markov matrix is then: {{0,3,0}, {0,0,4}, {1,1,1}} Equivalent matrix in standard form is: {{0, 1, 0}, {0, 0, 1}, {12, 4, 1}}
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FORMULA
| M = {{0, 1, 0}, {0, 0, 1}, {12, 4, 1}}; v(n)=M^n.v(0);v(0)={1,0,0}; a(n)=v(n)[[1]].
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MATHEMATICA
| Clear[M, v, f, g, x, n] M = {{0, 1, 0}, {0, 0, 1}, {12, 4, 1}} v[0] = {1, 0, 0} v[n_] := v[n] = M.v[n - 1] Table[v[n][[1]], {n, 0, 30}]
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CROSSREFS
| Sequence in context: A070710 A048759 A119877 * A003877 A161196 A111306
Adjacent sequences: A147830 A147831 A147832 * A147834 A147835 A147836
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Nov 14 2008
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