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Search: id:A134823
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| A134823 |
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A four person "hidden" player game: {a,b,c} are the observed players with 2 X 2 game value one Fibonacci payoff Matrix: MA={{0,1},{1,1}} The hidden player {d} in the middle has 4 X 4 payoff matrix: MB={{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {3, 0, 0, 7}} Characteristic Polynomial: 3 + 9 x - 8 x^3 + 20 x^4 + 6 x^5 - 38 x^6 + 5 x^7 + 21 x^8 - 10 x^9 + x^10; a plays with d;b plays with d, c plays with d, d plays with all. |
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| 4, 11, 63, 409, 2818, 19669, 137725, 965065, 6763525, 47403061, 332233597, 2328528748, 16319989180, 114382129186, 801671598205, 5618686762534, 39379767287245, 276001517369095, 1934415636331069, 13557765514528696
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OFFSET
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1,1
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COMMENT
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Ratio:7.00871 Total Game value [M]=-3/2
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FORMULA
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M = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 3, 0, 0, 7}}; v[0] = {1, 0, 1, 0, 1, 0, 0, 0, 0, 1}; v[n]=M.v[n-1] a(n) =Sum[v[n][[i]],{i,1,10}]
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MATHEMATICA
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M = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 3, 0, 0, 7}}; v[0] = {1, 0, 1, 0, 1, 0, 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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Sequence in context: A081073 A002831 A114053 this_sequence A000880 A006551 A151826
Adjacent sequences: A134820 A134821 A134822 this_sequence A134824 A134825 A134826
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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 28 2008
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