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A134250
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Three person "Quark" like Game as 9 X 9 Markov: MA1={{0,1,0},{0,0,1},{1,0,0}}: Det=1;gamevalue=-1/3 MA2={{0,0,1},{1,0,1},{0,1,0}}: Det=1;gamevalue=-1/3 MA3={{0,0,1},{0,2,0},{1,0,-3}}: Det=1;gamevalue=2/3 Characteristic Polynomial: -2 + 7 x - x^2 + 3 x^3 - 14 x^4 + 2 x^5 + 7 x^7 - x^8 -x^9.
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2
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4, 1, 7, -14, 55, -173, 580, -1907, 6307, -20822, 68779, -227153, 750244, -2477879, 8183887, -27029534, 89272495, -294847013, 973813540, -3216287627, 10622676427, -35084316902, 115875627139, -382711198313, 1264009222084, -4174738864559, 13788225815767
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Ratio approaches:-3.30278 First two matrices are permutations, so only the third matrix adds to the score overall. Designed for game values {-1/3,-1/3,2/3} being "Quark" like. Only thing good about it,is that this game gives a reference for the {-1/4,-1/4,1/2} game with the same starting vector. Other games of this sort give scores of 2^n+2 and 2^n+3 for MA3={{1,1,0},{0,1,0},{0,0,2}}.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (-2,4,-1).
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FORMULA
| a(n) = 2-17*(-1)^n*A006190(n) +5*(-1)^n*A006190(n+1). G.f. -x*(-4-9*x+7*x^2) / ( (x-1)*(x^2-3*x-1) ). - R. J. Mathar, Dec 06 2011
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MAPLE
| A006190 := proc(n)
coeftayl( x/(1-3*x-x^2), x=0, n) ;
end proc:
A134250 := proc(n)
2-17*(-1)^n*A006190(n)+5*(-1)^n*A006190(n+1) ;
end proc:
seq(A134250(n), n=1..10) ; # R. J. Mathar, Dec 06 2011
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MATHEMATICA
| M = {{0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 2, 0}, {0, 0, 0, 0, 0, 0, 1, 0, -3}}; v[0] = {0, 0, 1, 1, 0, 0, 1, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[Apply[Plus, v[n]], {n, 0, 50}]
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CROSSREFS
| Cf. A062709; A052548.
Sequence in context: A010643 A108906 A193842 * A139045 A084884 A143320
Adjacent sequences: A134247 A134248 A134249 * A134251 A134252 A134253
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KEYWORD
| uned,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 14 2008
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