login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A120723 Let M be the 8 X 8 matrix M = {{0, 1, 1, 0, 0, 1, 0, 0}, {1, 0, 0, 1, 1, 0, 0, 0}, {1, 0, 0, 1, 0, 1, 1, 0}, {0, 1, 1, 0, 1, 0, 1, 0}, {0, 1, 0, 1, 0, 1, 0, 1}, {1, 0, 1, 0, 1, 0, 0, 1}, {0, 0, 1, 1, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 1, 1, 0}}; let v[1] = [Fibonacci[1], ..., Fibonacci[8]]; let v[n] = M.v[n - 1]; then a(n) = v[n][[1]]. 0
1, 11, 63, 247, 887, 3207, 11383, 40679, 144663, 515719, 1835831, 6540327, 23289943, 82955975, 295436919, 1052244583, 3747563927, 13347268359, 47536758199, 169305160871, 602988299991, 2147576619847, 7648703663351 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

8 X 8 Markov chain for N4S4 and As4S4 which has D2d symmetry; characteristic polynomial = 16 - 56 x^2 + 16 x^3 + 45 x^4 - 8 x^5 - 14 x^6 + x^8.

One view of this structure is as a tetrahedron with a square plane in the middle of it.

REFERENCES

Cotton and Wilkinson, Advanced Inorganic Chemistry, Interscience Publishers, New York, 1966, page 533

LINKS

Table of n, a(n) for n=1..23.

FORMULA

G.f.: x*(1+3*x)*(1+6*x+16*x^2)/((1-x)*(1+2*x)*(1-3*x-2*x^2)). [Colin Barker, Apr 04 2012]

MATHEMATICA

M = {{0, 1, 1, 0, 0, 1, 0, 0}, {1, 0, 0, 1, 1, 0, 0, 0}, {1, 0, 0, 1, 0, 1, 1, 0}, {0, 1, 1, 0, 1, 0, 1, 0}, {0, 1, 0, 1, 0, 1, 0, 1}, {1, 0, 1, 0, 1, 0, 0, 1}, {0, 0, 1, 1, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 1, 1, 0}}; v[1] = Table[Fibonacci[n], {n, 1, 8}]; v[n_] := v[n] = M.v[n - 1]; a = Table[Floor[v[n][[1]]], {n, 1, 50}]

CoefficientList[Series[(1 + 3 x)*(1 + 6 x + 16 x^2)/((1 - x)*(1 + 2 x)*(1 - 3 x - 2 x^2)), {x, 0, 50}], x] (* Bruno Berselli, Apr 04 2012 *)

CROSSREFS

Sequence in context: A162946 A301610 A298046 * A053367 A163706 A180763

Adjacent sequences:  A120720 A120721 A120722 * A120724 A120725 A120726

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Aug 17 2006

EXTENSIONS

Edited by N. J. A. Sloane, Jun 15 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 16 23:49 EDT 2019. Contains 325092 sequences. (Running on oeis4.)