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Search: id:A122167
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| A122167 |
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Steinbach 4 X 4 minus the Indentity matrix to give a new vector matrix Markov with a characteristic polynomial of: -2 + 7 x - 3 x^2 - 2 x^3 + x^4. |
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+0
2
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| 1, -3, 3, -11, 10, -40, 33, -146, 107, -535, 339, -1968, 1040, -7267, 3040, -26937, 8195, -100235, 18754, -374436, 25425, -1404206, -73577, -5286619, -913677, -19980584, -5843020, -75805291, -31102908, -288681717, -151721161, -1103377699, -703352678, -4232153760, -3154163983
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Remember? 1/(1-x)=Sum[x^n,{n,0,Infinitity}] So to try with the Steinbach field: (I-A[i,j])^(-1)=Sun[A[i,j]^n,{n,0,Infinity}] It doesn't appear it shoulsd be finite? But I-A[i,j] is finite--> zero? {{1,0,0}, {{1,1,1}, {{0,-1,-1}, {0,1,0}, {1,1,0}, {-1,0,0}, {0,0,1}} - 1,0,0}}= { -1,0,1}}
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REFERENCES
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P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.
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FORMULA
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M = {{0, -1, -1, -1}, {-1, 0, -1, 0}, {-1, -1, 1, 0}, {-1, 0, 0, 1}}; v[1] = {1, 1, 1, 1}; 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, -1, 0}, {-1, -1, 1, 0}, {-1, 0, 0, 1}}; v[1] = {1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
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CROSSREFS
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Cf. A046854. Cf. A046854. Cf. A007700, A059455. Cf. A065941.
Sequence in context: A036391 A073106 A107229 this_sequence A095019 A068594 A122573
Adjacent sequences: A122164 A122165 A122166 this_sequence A122168 A122169 A122170
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KEYWORD
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uned,sign
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AUTHOR
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Gary Adamson and Roger Bagula (qntmpkt(AT)yahoo.com), Oct 17 2006
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