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A134884 A three person Markov game designed to have a limiting ratio near 1/Alpha: Ma matrix=Mb = {{0, 1}, {-67, -67}}; game value =-67; Mc={{0, 1, 0}, {0, 0, 1}, {134, 0, 137}}: game value=134; Total matrix game value=-601526; Characteristic Polynomial: 601526 + 1203052 x + 1234475 x^2 + 1243453 x^3 + 624507 x^4 + 13735 x^5 + 3 x^6-x^7. 0
3, 1, 27269, 1954390, 385327519, 45035320119, 6682022825588, 881709781234437, 123029167626415695, 16708818725606483602, 2298930844925022134207, 314329661992199488247899, 43107655899059704928917636 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Relative game value=(Game value Ma/Game value Mc)=-67/134=-1/2; Limiting ratio is: 137.00713868806855 Current value of 1/Alpha: 137.03599679 This hidden person game model is of two spin 1/2 particles interacting through a third hidden particle with a limiting constant of very near 1/Alpha.
LINKS
FORMULA
M = {{0, 1, 0, 0, 0, 0, 0}, {-67, -67, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 134, 0, 137, 0, 0}, {0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -67, -67}}; v[0] = {1, 0, 1, 0, 0, 0, 1}; v[n]=M.v[n-1] a(n) = Sum[v[n][[i]],{i,1,7}]
G.f.: -x*(8844*x^4 +8509*x^3 -137*x^2 -209*x +3)/((67*x^2 +67*x +1)*(134*x^3 +137*x -1)). [Colin Barker, Nov 02 2012]
MATHEMATICA
M = {{0, 1, 0, 0, 0, 0, 0}, {-67, -67, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 134, 0, 137, 0, 0}, {0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, -67, -67}}; v[0] = {1, 0, 1, 0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[Apply[Plus, v[n]], {n, 0, 50}]
CROSSREFS
Sequence in context: A068542 A036112 A266230 * A229850 A269162 A033909
KEYWORD
nonn,uned,easy
AUTHOR
Roger L. Bagula, Jan 29 2008
STATUS
approved

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Last modified May 20 14:08 EDT 2024. Contains 372717 sequences. (Running on oeis4.)