|
Search: id:A120469
|
|
|
| A120469 |
|
14 X 14 face centered cubic bonding Matrix Markov. |
|
+0
1
|
|
| 1, 5, 34, 240, 1755, 12787, 93549, 683653, 4999040, 36546925, 267210674, 1953631757, 14283593763, 104431164565, 763525632740, 5582346722921, 40814089880858, 298403135454915, 2181708201960095, 15951074407242085
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
This structure is one of the basic metal crystal structures ( Au,Ag,Cu) and the characteristic polynomial gives all real energy levels. x*(x+3)*(-16-140x-2x^2+968x^3+830x^4-946x^5-982x^6+239x^7+351x^8+5x^9-39x^10-3*x^11+x^12) {-3.04986, -3., -2.51223, -1.81761, -1.43756, -0.844658, -0.471031, -0.126922, 0., 0.405946, 1.23527, 1.58663, 2.72075, 7.31128} Ratio=a[n+1)/a[n]=7.31128
|
|
REFERENCES
|
http://cst-www.nrl.navy.mil/lattice/struk/a1.html
|
|
FORMULA
|
M = {{0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1}, {1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0}, {0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0}, {1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1}, {0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0}, {0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1}, {0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1}, {1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1}, {1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0}, {0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1}, {0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1}, {0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1}, {0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1}, {1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0}} v[1] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} v[n_] := v[n] = M.v[n - 1] a(n) = v[n][[1]]
|
|
MATHEMATICA
|
M = {{0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1}, {1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0}, {0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0}, {1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1}, {0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0}, {0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1}, {0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1}, {1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1}, {1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0}, {0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1}, {0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1}, {0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1}, {0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1}, {1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0}} v[1] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}] Det[M - x*IdentityMatrix[14]] Factor[%] aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[14]] == 0, x][[n]], { n, 1, 14}] ListPlot[aaa] Abs[aaa] a1 = Table[N[a[[n]]/a[[n - 1]]], {n, 7, 50}]
|
|
CROSSREFS
|
Sequence in context: A015545 A102436 A033889 this_sequence A066559 A073279 A080503
Adjacent sequences: A120466 A120467 A120468 this_sequence A120470 A120471 A120472
|
|
KEYWORD
|
nonn,uned
|
|
AUTHOR
|
Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Jul 04 2006
|
|
|
Search completed in 0.002 seconds
|
