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Search: id:A121803
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| A121803 |
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Bonding graph 12 X 12 hyper-tetrahedron -torus ( 3 cycle) made by adding 4 connection in the graph to the dual-hpyer-tetrahedron: Characteristic polynomial: (-2 + x)(-1 + x)^2(2 + x)^5(-13 + 19 x + 2x^2 - 6x^3 + x^4). |
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+0
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| 0, 28, 432, 2083, 11262, 54976, 274107, 1345543, 6629946, 32586349, 160268532, 787926091, 3874117269, 19047230005, 93648237255, 460429207264, 2263745709876, 11129911057732, 54721250218635, 269042081326366
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This adding of connections raises the secular total energy from -19.8998 units to -23.4555 units. aaa = Table[ x /. NSolve[Det[M - x*IdentityMatrix[12]] == 0, x][[n]], {n, 1, 12}] 2*Sum[aaa[[n]], {n, 1, 6}] The question raised by these dual -hyper-Platonics is that one can "close the cycle" and make them tori, but that pretty much would say that they become "closed strings" instead of open ones. This raises a fundamental one of symmetry... they are more symmetrical closed, but that implies a physical reality that may not be true. hyper: (4d) Present-> Past/ Future dual-Hyper (5d) Past-> Present -> Future Cycle ( or string closed) Past -> Present ->Future-> Past I can make up the bonding graphs, the mathematicall models but are they better or worse representations of the physics?
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FORMULA
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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, 1, 0, 0, 0}, {0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0}, {0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0}, {0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 01}, {0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1}, {0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 1, 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]]
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MATHEMATICA
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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, 1, 0, 0, 0}, {0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0}, {0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0}, {0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 01}, {0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1}, {0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1}, {0, 0, 0, 1, 0, 0, 0, 1, 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}]
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CROSSREFS
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Sequence in context: A004415 A096949 A093974 this_sequence A022656 A125485 A054337
Adjacent sequences: A121800 A121801 A121802 this_sequence A121804 A121805 A121806
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Aug 28 2006
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