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A133381 Vector Matrix Markov designed so that the matrix row sums are all zero: characteristic polynomial: -3149685x - 88636 x^2 + 1037 x^3 + x^4. 0
0, -1, 5, -90986, 91645977, -103085764820, 114736493696302, -127830197854583449, 142405011343301378985, -158642970366894551628139, 176732345999164897395531038, -196884390194421237873409045085, 219334285467476751254430593851098 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

It is certainly an off the wall model where the Turing symbol number and tape reading are used as combinatorial "information" for the Markov matrix. The d information is Boson like and the h information is Fermion like, making the alpha information Matter/ Antimatter like in a SU(7) or A_6 model of the Chaitan "universe". Root structure is: { -1114.03, -27.1418, 0, 104.168}

LINKS

Table of n, a(n) for n=1..13.

Index entries for linear recurrences with constant coefficients, signature (-1037,88636,3149685).

FORMULA

a0=Binomial[46,2]+Binomial[4,2]-Binomial[49,2]; b0=Binomial[46,3]+Binomial[4,3]-Binomial[49,3]; M = {{1, 1, -1, -1}, {49, 1, -46, -4}, {Binomial[49, 2], a0, -Binomial[46, 2], -Binomial[4, 2]}, {Binomial[49, 3], b0, -Binomial[46, 3], -Binomial[4, 3]}}; v(n)=M*v(n-1); a(n) = v(n)[[1]]

G.f.: -x^2*(2835*x^2-1032*x-1)/(3149685*x^3+88636*x^2-1037*x-1). [Colin Barker, Nov 14 2012]

EXAMPLE

system equations:O=omega; A=alpha

O+d=A+h

49*O+d=46*A+4*d

Binomial[49,2]*O+a0*d=Binomial[46,2]*A+Binomial[4,2]*h

Binomial[49,3]*O+b0*d=Binomial[46,3]*A+Binomial[4,3]*h

a0,b0 adjusted to give zero row sum or constant information in a 3,2

universal Turing machine system.

MATHEMATICA

a0 = Binomial[46, 2] + Binomial[4, 2] - Binomial[49, 2]; b0 = Binomial[46, 3] + Binomial[4, 3] - Binomial[49, 3]; M = {{1, 1, -1, -1}, {49, 1, -46, -4}, {Binomial[49, 2], a0, -Binomial[46, 2], -Binomial[4, 2]}, {Binomial[49, 3], b0, -Binomial[46, 3], -Binomial[4, 3]}}; v[0] = {0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[v[n][[1]], {n, 0, 20}]

CROSSREFS

Sequence in context: A145232 A263174 A123591 * A236066 A151589 A243114

Adjacent sequences:  A133378 A133379 A133380 * A133382 A133383 A133384

KEYWORD

uned,sign,easy

AUTHOR

Roger L. Bagula, Oct 28 2007

STATUS

approved

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Last modified September 20 20:02 EDT 2020. Contains 337265 sequences. (Running on oeis4.)