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A122173
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Steinbach 6 X 6 minus the identity matrix to give a new vector matrix Markov with a characteristic polynomial of: -1 + 12 x - 34 x^2 + 30 x^3 - 6 x^4 - 3 x^5 + x^6.
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0
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1, -5, 10, -45, 110, -421, 1148, -4037, 11697, -39250, 117736, -384657, 1177235, -3787218, 11727187, -37389217, 116571621, -369712938, 1157315631, -3659226205, 11481436216, -36237006073, 113856243558, -358967583724, 1128781753801, -3556642214960, 11189229179710
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.
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FORMULA
| M = {{0, -1, -1, -1, -1, -1}, {-1, 0, -1, -1, -1, 0}, {-1, -1, 0, -1, 0, 0}, {-1, -1, -1, 1, 0, 0}, {-1, -1, 0, 0, 1, 0}, {-1, 0, 0, 0, 0, 1}}; v[1] = {1, 1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a(n) = v[n][[1]]
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MATHEMATICA
| M = {{0, -1, -1, -1, -1, -1}, {-1, 0, -1, -1, -1, 0}, {-1, -1, 0, -1, 0, 0}, {-1, -1, -1, 1, 0, 0}, {-1, -1, 0, 0, 1, 0}, {-1, 0, 0, 0, 0, 1}}; v[1] = {1, 1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[Floor[v[n][[1]]], {n, 1, 50}]
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CROSSREFS
| Cf. A046854. Cf. A046854. Cf. A007700, A059455. Cf. A065941.
Sequence in context: A136138 A186031 A187877 * A083515 A103971 A035406
Adjacent sequences: A122170 A122171 A122172 * A122174 A122175 A122176
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KEYWORD
| uned,sign
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AUTHOR
| Gary Adamson and Roger Bagula (qntmpkt(AT)yahoo.com), Oct 17 2006
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