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Search: id:A135644
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| A135644 |
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Polynomial expansion of 36by36 6 person "pyramidal" saciety structure game: Followers: level one pay off matrix Ma={{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 1}}; characteristic polynomial: (-1 - x^5 +x^6) level two pay off matrix Mb={{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 2}}; characteristic polynomial: (-1 - 2*x^5 +x^6); Leader Payoff matrix: Mc={{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {9, 0, 0, 0, 0, 34}}; characteristic polynomial: (-9 - 34x^5 + x^6) Expansion of polynomial:(1/(1 - 40 x + 218 x^2 - 492 x^3 + 553 x^4 - 308 x^5 + 54 x^6 + 248 x^7 - 984 x^8 + 1604 x^9 - 1178 x^10 + 324 x^11 + 55 x^12 - 592 x^13 + 1644 x^14 - 1732 x^15 + 625 x^16 - 100 x^18 + 688 x^19 - 1208 x^20 + 620 x^21 + 95 x^24 - 392 x^25 + 330 x^26 - 46 x^30 + 88 x^31 + 9 x^36)). |
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| 1, 40, 1382, 47052, 1599931, 54398036, 1849534086, 62884161136, 2138061495013, 72694091262236, 2471599117332784, 84034370478932992, 2857168612929602684, 97143733405564093636, 3302886955031732949874, 112298157125325742290668
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OFFSET
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1,2
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COMMENT
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Limiting ratio is:34.00000019808332
This sequence represents the Matrix Markov of the 36by36 game matrix
of a six person game with pyramidal or Hierarchical structure.
It appear to be the lowest possible such game with multiple values.
Not effort was made to use the whole 36by36 matrix made up of six 6by6
matrices of three types.
The idea is that ancient societies had a structure of poor to rich
in a relative pyramid. Here the lowest level get the smallest payoffs, the intermediate gets more and the leader gets the highest payoff.
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FORMULA
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a(n) = Expansion(1/(1 - 40 x + 218 x^2 - 492 x^3 + 553 x^4 - 308 x^5 + 54 x^6 + 248 x^7 - 984 x^8 + 1604 x^9 - 1178 x^10 + 324 x^11 + 55 x^12 - 592 x^13 + 1644 x^14 - 1732 x^15 + 625 x^16 - 100 x^18 + 688 x^19 - 1208 x^20 + 620 x^21 + 95 x^24 - 392 x^25 + 330 x^26 - 46 x^30 + 88 x^31 + 9 x^36))
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MATHEMATICA
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f[x_] = (-1 - x^5 + x^6)^4*(-1 - 2*x^5 + x^6)*(-9 - 34x^5 + x^6); g[x_] = Expand[x^36*f[1/x]]; a = Table[ SeriesCoefficient[Series[1/g[x], {x, 0, 30}], n], {n, 0, 30}]
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CROSSREFS
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Adjacent sequences: A135641 A135642 A135643 this_sequence A135645 A135646 A135647
Sequence in context: A061650 A006101 A049396 this_sequence A063820 A009984 A041761
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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 31 2008
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