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<a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4, 13, -44, -57, 120, 63, -56, 6).

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_Roger L. Bagula_, Aug 26 2006

LinearRecurrence[{4, 13, -44, -57, 120, 63, -56, 6}, {0, 28, 408, 1502, 7821, 31911, 145162, 616196}, 30] (* From _Harvey P. Dale, _, Feb 29 2012 *)

_Roger Bagula (rlbagulatftn(AT)yahoo.com), _, Aug 26 2006

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LinearRecurrence[{4, 13, -44, -57, 120, 63, -56, 6}, {0, 28, 408, 1502, 7821, 31911, 145162, 616196}, 30] (* From Harvey P. Dale, Feb 29 2012 *)

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Dual-Hyper-tetrahedron bonding graph 12 X 12 matrix markov: One hyper-tetrahedron in the time direction and one in the Kaluza -Klein tau direction to give a broken symmetry 5 dimensional Platonic model:( with blocks of 4 X 4 zero matrices) Characteristic Polynomial: (-3 + x)(1 +x)^3(-1 + 2 x + x^2)^2(-2 + 16 x - 5 x^2 - 4 x^3 + x^4).

a(n)= 4*a(n-1) +13*a(n-2) -44*a(n-3) -57*a(n-4) +120*a(n-5) +63*a(n-6) -56*a(n-7) +6*a(n-8).

It has become clear that to understand current physics we have to extend our geometric models past four dimension to five. The concept of a dual-hyper- Platonic bonding graph allows one without a specific group theory gauge group to find a secular equation with relative energy states.

M = {{0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0}, {1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0}, {1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0}, {1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1}, { 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0}, {0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 01}, {0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1}, {0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0}} v[1] = Table[Fibonacci[n], {n, 0, 11}] v[n_] := v[n] = M.v[n - 1] a(n) = v[n][[1]]

G.f.: x^2*(-28-296*x+494*x^2+2259*x^3-649*x^4-1829*x^5+281*x^6)/( (3*x-1) * (1+x) * (x^2-2*x-1) * (2*x^4-16*x^3+5*x^2+4*x-1)). [Oct 14 2009]

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Definition replaced by recurrence - The Assoc. Editors of the OEIS, Oct 14 2009

Dual-Hyper-tetrahedron bonding graph 12by12 12 X 12 matrix markov: One hyper-tetrahedron in the time direction and one in the Kaluza -Klein tau direction to give a broken symmetry 5 dimensional Platonic model:( with blocks of 4by4 4 X 4 zero matrices) Characteristic Polynomial: (-3 + x)(1 +x)^3(-1 + 2 x + x^2)^2(-2 + 16 x - 5 x^2 - 4 x^3 + x^4).

nonn,uned,new

Roger Bagula (rlbagularlbagulatftn(AT)sbcglobalyahoo.netcom), Aug 26 2006

Dual-Hyper-tetrahedron bonding graph 12by12 matrix markov: One hyper-tetrahedron in the time direction and one in the Kaluza -Klein tau direction to give a broken symmetry 5 dimensional Platonic model:( with blocks of 4by4 zero matrices) Characteristic Polynomial: (-3 + x)(1 +x)^3(-1 + 2 x + x^2)^2(-2 + 16 x - 5 x^2 - 4 x^3 + x^4).

0, 28, 408, 1502, 7821, 31911, 145162, 616196, 2706385, 11640499, 50598522, 218517332, 946752849, 4093542243, 17716803778, 76627964684, 331523693857, 1434000301795, 6203258085066, 26832402306020, 116067057052689

1,2

It has become clear that to understand current physics we have to extend our geometric models past four dimension to five. The concept of a dual-hyper- Platonic bonding graph allows one without a specific group theory gauge group to find a secular equation with relative energy states.

M = {{0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0}, {1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0}, {1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0}, {1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1}, { 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0}, {0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 01}, {0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1}, {0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0}} v[1] = Table[Fibonacci[n], {n, 0, 11}] v[n_] := v[n] = M.v[n - 1] a(n) = v[n][[1]]

M = {{0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0}, {1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0}, {1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0}, {1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1}, { 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0}, {0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 01}, {0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1}, {0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0}} v[1] = Table[Fibonacci[n], {n, 0, 11}] v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}] Det[M - x*IdentityMatrix[12]] Factor[%] aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[12]] == 0, x][[n]], {n, 1, 12}]

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Roger Bagula (rlbagula(AT)sbcglobal.net), Aug 26 2006

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