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Search: id:A133931
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| A133931 |
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A 4 X 4 vector Markov of a Fibonacci game matrix MA and an anti-Fibonacci game matrix MB such that game_valueMa+game_ValueMB =0 and the score is the sum of the vector out put of the Markov: MA={{0,1},{1,1}}; MB={{1,0},{3,1}}; Characteristic Polynomial is: -1 + x + 2 x^2 - 3 x^3 + x^4. |
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+0
1
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| 2, 6, 10, 15, 21, 29, 40, 56, 80, 117, 175, 267, 414, 650, 1030, 1643, 2633, 4233, 6820, 11004, 17772, 28721, 46435, 75095, 121466, 196494, 317890, 514311, 832125, 1346357, 2178400, 3524672, 5702984, 9227565, 14930455, 24157923, 39088278
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This approach to a two person game games theory is inspired by the TV shoe Numb3rs where the hero publishes a book on interpersonal games theory. In this game one persons seems to be losing all the time, but there is actually a balance of overall score long term. The result presents a games theory paradox like that of the prisoner's dilemma.
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FORMULA
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M = {{0, 1, 0, 0}, {1, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 3, 1}}; v[1] = {0, 1, 1, 0}; v[n_] := v[n] = M.v[n - 1] a(n) = Sum[v(i),{i,1,4}]
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MATHEMATICA
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M = {{0, 1, 0, 0}, {1, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 3, 1}}; v[1] = {0, 1, 1, 0}; v[n_] := v[n] = M.v[n - 1] a = Table[Apply[Plus, v[n]], {n, 1, 50}]
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CROSSREFS
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Sequence in context: A118369 A082816 A074105 this_sequence A050895 A097022 A137236
Adjacent sequences: A133928 A133929 A133930 this_sequence A133932 A133933 A133934
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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 08 2008
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