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Search: id:A134884
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| A134884 |
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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. |
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| 3, 1, 27269, 1954390, 385327519, 45035320119, 6682022825588, 881709781234437, 123029167626415695, 16708818725606483602, 2298930844925022134207, 314329661992199488247899, 43107655899059704928917636
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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Wikipedia, Fine Structure Constant
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FORMULA
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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}]
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MATHEMATICA
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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}]
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CROSSREFS
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Adjacent sequences: A134881 A134882 A134883 this_sequence A134885 A134886 A134887
Sequence in context: A049330 A068542 A036112 this_sequence A033909 A133949 A139808
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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 29 2008
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