A135649 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}.

-1, -59, -2951, -144881, -7100318, -347919854, -17048087778, -835356351147, -40932461369999, -2005690607714190, -98278839782943427, -4815663149532534269, -235967494335111673276, -11562407222812624781054, -566557953937031952348408, -27761339743856012706314735

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..16.

Formula

(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)).

Mathematica

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}]

Crossrefs

Sequence in context: A017722 A263508 A119886 * A278367 A198509 A258269

Adjacent sequences: A135646 A135647 A135648 * A135650 A135651 A135652

Keyword

uned,sign

Author

Roger L. Bagula, Jan 31 2008

Status

approved