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Search: id:A134326
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| A134326 |
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A 9 X 9 Matrix vector sum Markov sequence with characteristic polynomial: -5 x - 8 x^2 + 42 x^3 + 37 x^4 - 19 x^5 - 23 x^6 + 5 x^7 + 4 x^8 - x^9 Largest root/ratio is 3.23322. |
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+0
4
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| 3, 11, 34, 112, 359, 1167, 3764, 12191, 39391, 127434, 411973, 1332290, 4307638, 13928919, 45036841, 145621921, 470842799, 1522389829, 4922341763, 15915370482, 51458800352, 166380151440, 537950254595, 1739329494378
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The root structure is nearly all semi-unique algebriac real irrationals: NSolve[CharacteristicPolynomial[M, x] == 0, x] {{x -> -1.71677}, {x -> -1.08312 - 0.612998 I}, {x -> -1.08312 + 0.612998I}, {x -> -0.296126}, {x -> 0.}, {x -> 0.394603}, {x -> 1.82647}, {x -> 2.72485}, {x -> 3.23322}} The game value of the matrix is: Det[M]/(Sum[Sum[If[i == j, M[[i, j]], 0], {i, 1, 9}], {j, 1, 9}] - Sum[Sum[If[i == j, 0, M[[i, j]]], {i, 1, 9}], {j, 1, 9}])=0 zero
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FORMULA
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M = {{0, 1, 0, 1, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 1, 0, 0, 1, 0}, {1, 0, 0, 0, 0, 1, 0, 0, 1}, {1, 0, 0, 0, 1, 0, 1, 0, 0}, {0, 1, 0, 1, 0, 0, 0, 1, 0}, {0, 0, 1, 0, 1, 0, 0, 0, 1}, {1, 0, 0, 1, 0, 0, 1, 1, 0}, {0, 1, 0, 0, 1, 0, 0, 1, 0}, {0, 0, 1, 0, 0, 1, 0, 0, 2}}; v[0] = {1, 0, 0, 0, 1, 0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a(n) = Sum[v[n][[i]],{i,1,9}]
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MATHEMATICA
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M = {{0, 1, 0, 1, 0, 0, 1, 0, 0}, {0, 0, 1, 0, 1, 0, 0, 1, 0}, {1, 0, 0, 0, 0, 1, 0, 0, 1}, {1, 0, 0, 0, 1, 0, 1, 0, 0}, {0, 1, 0, 1, 0, 0, 0, 1, 0}, {0, 0, 1, 0, 1, 0, 0, 0, 1}, {1, 0, 0, 1, 0, 0, 1, 1, 0}, {0, 1, 0, 0, 1, 0, 0, 1, 0}, {0, 0, 1, 0, 0, 1, 0, 0, 2}}; v[0] = {1, 0, 0, 0, 1, 0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[Apply[Plus, v[n]], {n, 0, 50}]
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CROSSREFS
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Adjacent sequences: A134323 A134324 A134325 this_sequence A134327 A134328 A134329
Sequence in context: A084266 A052471 A037496 this_sequence A094308 A057838 A088578
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 16 2008
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