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A120469 14 X 14 face centered cubic bonding Matrix Markov. 0
1, 5, 34, 240, 1755, 12787, 93549, 683653, 4999040, 36546925, 267210674, 1953631757, 14283593763, 104431164565, 763525632740, 5582346722921, 40814089880858, 298403135454915, 2181708201960095, 15951074407242085 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (0,48,112,-366,-1292,265,3892,2008,-3458,-2902,146,436,48).

FORMULA

G.f.: -(20*x^12 +184*x^11 +121*x^10 -915*x^9 -1524*x^8 -132*x^7 +1068*x^6 +581*x^5 -71*x^4 -112*x^3 -14*x^2 +5*x +1) / ((3*x +1)*(16*x^12 +140*x^11 +2*x^10 -968*x^9 -830*x^8 +946*x^7 +982*x^6 -239*x^5 -351*x^4 -5*x^3 +39*x^2 +3*x -1)). - Colin Barker, May 17 2013

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: A102436 A291027 A033889 * A180909 A183415 A066559

Adjacent sequences:  A120466 A120467 A120468 * A120470 A120471 A120472

KEYWORD

nonn,uned,easy

AUTHOR

Roger L. Bagula and Gary W. Adamson, Jul 04 2006

STATUS

approved

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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)