The On-Line Encyclopedia of Integer Sequences (OEIS)

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A122603

Expansion of x*(1-42*x+650*x^2-4477*x^3+12896*x^4-11417*x^5+2675*x^6+110*x^7) / ( 1-43*x+691*x^2-5146*x^3+17903*x^4-25954*x^5+11826*x^6-876*x^7+x^8 )
(history; published version)

#11 by N. J. A. Sloane at Sun Mar 19 13:56:39 EDT 2017

STATUS

editing

approved

#10 by N. J. A. Sloane at Sun Mar 19 13:56:36 EDT 2017

REFERENCES

P. Steinbach, Field Guide to Simple Graphs. Design Lab, Albuquerque NM, 1990.

STATUS

approved

editing

#9 by Charles R Greathouse IV at Sat Jun 13 00:52:09 EDT 2015

LINKS

<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (43,-691,5146,-17903,25954,-11826,876,-1)

Discussion

Sat Jun 13

00:52

OEIS Server: https://oeis.org/edit/global/2439

#8 by Charles R Greathouse IV at Fri Jun 12 15:26:07 EDT 2015

LINKS

<a href="/index/Rea#recLCCRec">Index to sequences with linear recurrences with constant coefficients</a>, signature (43,-691,5146,-17903,25954,-11826,876,-1)

Discussion

Fri Jun 12

15:26

OEIS Server: https://oeis.org/edit/global/2436

#7 by Charles R Greathouse IV at Fri Oct 12 14:55:29 EDT 2012

AUTHOR

_Roger L. Bagula _ and _Gary W. Adamson (rlbagulatftn(AT)yahoo.com), _, Sep 20 2006

Discussion

Fri Oct 12

14:55

OEIS Server: https://oeis.org/edit/global/1841

#6 by R. J. Mathar at Mon Nov 07 12:52:14 EST 2011

STATUS

editing

approved

#5 by R. J. Mathar at Mon Nov 07 12:52:04 EST 2011

COMMENTS

Obtained as the top element of the vector resulting from multiplying the n-th power of the 8 X 8 matrix [[0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1], [-1, -4, 10, 10, -15, -6, 7, 1]] with the column vector which contains only 1's.

STATUS

proposed

editing

#4 by R. J. Mathar at Mon Nov 07 07:16:56 EST 2011

STATUS

editing

proposed

#3 by R. J. Mathar at Mon Nov 07 07:16:41 EST 2011

NAME

8 X 8 Vector Matrix Markov for Steinbach characteristic polynomial: Expansion of x*(1 -42*x+650*x^2-4477*x^3+ 12896*x^4 -11417*x^5+2675*x^6+110*x ^7) / ( 1- 10 43*x+691*x^2 - 10 5146*x^3 + 15 17903*x^4 + 6 -25954*x^5 - 7 +11826*x^6 - 876*x^7 +x^8. )

COMMENTS

Obtained as the top element of the vector resulting from multiplying the 8 X 8 matrix [[0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1], [-1, -4, 10, 10, -15, -6, 7, 1]] with the column vector which contains only 1's.

LINKS

<a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (43,-691,5146,-17903,25954,-11826,876,-1)

FORMULA

M = {{0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {-1, -4, 10, 10, -15, -6, 7, 1}}; v[1] = Table[1, {n, 1, 8}]; v[n_] := v[n] = M.v[n - 1] a(n) = v[n][[1]]

CROSSREFS

Cf. A066170.

KEYWORD

nonn,unedless

STATUS

approved

editing

#2 by N. J. A. Sloane at Fri May 11 03:00:00 EDT 2007

NAME

8by8 8 X 8 Vector Matrix Markov for Steinbach characteristic polynomial: 1 + 4 x - 10 x^2 - 10 x^3 + 15 x^4 + 6 x^5 - 7 x^6 - x^7 +x^8.

KEYWORD

nonn,uned,new

AUTHOR

Roger Bagula and Gary Adamson (rlbagularlbagulatftn(AT)sbcglobalyahoo.netcom), Sep 20 2006