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%I #3 Mar 30 2012 17:34:22
%S -1,-59,-2951,-144881,-7100318,-347919854,-17048087778,-835356351147,
%T -40932461369999,-2005690607714190,-98278839782943427,
%U -4815663149532534269,-235967494335111673276,-11562407222812624781054,-566557953937031952348408,-27761339743856012706314735
%N Seven-person pyramidal game with four payoff matrices: expansion of the 49by49 matrix characteristic polynomial: p(x)=(1 + x^6 - x^7)^3(1 + 2 x^6 - x^7)^2(1 + 3 x^6 - x^7)(23 + 49 x^6 -x^7) f(x)=1/(x^49*p(1/x)) Weights: 7->{1,1,2,3}.
%C Ratio approaches:49.00000000166169
%C Follower matrices:
%C Ma={{0, 1, 0, 0, 0, 0, 0},
%C {0, 0, 1, 0, 0, 0, 0},
%C {0, 0, 0, 1, 0, 0, 0},
%C {0, 0, 0, 0, 1, 0, 0},
%C {0, 0, 0, 0, 0, 1, 0},
%C {0, 0, 0, 0, 0, 0, 1},
%C {1, 0, 0, 0, 0, 0, a}}; a={1,2,3};
%C M_Leader={{0, 1, 0, 0, 0, 0, 0},
%C {0, 0, 1, 0, 0, 0, 0},
%C {0, 0, 0, 1, 0, 0, 0},
%C {0, 0, 0, 0, 1, 0, 0},
%C {0, 0, 0, 0, 0, 1, 0},
%C {0, 0, 0, 0, 0, 0, 1},
%C {23, 0, 0, 0, 0, 0, 49}}
%C I missed this game in my first round of analysis.
%F (x)=(1 + x^6 - x^7)^3(1 + 2 x^6 - x^7)^2(1 + 3 x^6 - x^7)(23 + 49 x^6 -x^7) f(x)=1/(x^49*p(1/x)) a(n) =expansion(f(x)).
%t f[x_] = Product[CharacteristicPolynomial[{{0, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, a}}, x]^(4 - a), {a, 1, 3}]*CharacteristicPolynomial[{{0, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 1}, {23, 0, 0, 0, 0, 0, 49}}, x]; g[x_] = Expand[x^49*f[1/x]]; a = Table[ SeriesCoefficient[Series[1/g[x], {x, 0, 30}], n], {n, 0, 30}]
%K uned,sign
%O 1,2
%A _Roger L. Bagula_, Jan 31 2008
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