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Search: id:A135649
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| A135649 |
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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}. |
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+0
1
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| -1, -59, -2951, -144881, -7100318, -347919854, -17048087778, -835356351147, -40932461369999, -2005690607714190, -98278839782943427, -4815663149532534269, -235967494335111673276, -11562407222812624781054, -566557953937031952348408, -27761339743856012706314735
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Ratio approaches:49.00000000166169
Follower matrices:
Ma={{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}}; a={1,2,3};
M_Leader={{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}}
I missed this game in my first round of analysis.
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FORMULA
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(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)).
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MATHEMATICA
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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}]
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CROSSREFS
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Sequence in context: A017775 A017722 A119886 this_sequence A094489 A093403 A087535
Adjacent sequences: A135646 A135647 A135648 this_sequence A135650 A135651 A135652
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KEYWORD
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uned,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 31 2008
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