The On-Line Encyclopedia of Integer Sequences (OEIS)

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A005822

G.f.: x*(1-x^2)*(x^4+x^3-x^2+x+1) / (x^8-4*x^6-x^4-4*x^2+1).
(history; published version)

#45 by Charles R Greathouse IV at Thu Sep 08 08:44:34 EDT 2022

PROG

(MAGMAMagma) m:=40; R<x>:=PowerSeriesRing(Rationals(), m); [0] cat Coefficients(R!( x*(1-x^2)*(x^4+x^3-x^2+x+1) / (x^8-4*x^6-x^4-4*x^2+1))); // Vincenzo Librandi, Jan 28 2020

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#44 by Charles R Greathouse IV at Wed Apr 13 13:25:17 EDT 2022

LINKS

Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Discussion

Wed Apr 13

13:25

OEIS Server: https://oeis.org/edit/global/2938

#43 by Charles R Greathouse IV at Fri Mar 12 22:32:36 EST 2021

LINKS

Simon Plouffe, <a href="https://arxiv.org/ftp/arxiv/papers/0911abs/0911.4975.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

Discussion

Fri Mar 12

22:32

OEIS Server: https://oeis.org/edit/global/2898

#42 by N. J. A. Sloane at Mon Feb 22 14:14:30 EST 2021

LINKS

Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articlesA000051/FonctionsGeneratricesa000051_2.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, Appendix to Thesis, Montreal, 1992.

Discussion

Mon Feb 22

14:14

OEIS Server: https://oeis.org/edit/global/2888

#41 by N. J. A. Sloane at Mon Feb 22 12:12:22 EST 2021

LINKS

Simon Plouffe, <a href="httphttps://www.lacim.uqamarxiv.caorg/ftp/arxiv/%7Eplouffepapers/articles0911/MasterThesis0911.4975.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

Discussion

Mon Feb 22

12:12

OEIS Server: https://oeis.org/edit/global/2887

#40 by N. J. A. Sloane at Thu Feb 06 09:10:05 EST 2020

STATUS

editing

approved

#39 by N. J. A. Sloane at Thu Feb 06 09:09:58 EST 2020

COMMENTS

The original definition was "Number of spanning trees in third power of cycle", but even after studying Baron et al. (1985) this is unclear, so the definition has been replaced by the generating function.

This is a rescaled version of the number of spanning trees in the cube of an n-cycle. See A331905 for details. - N. J. A. Sloane, Feb 06 2020

LINKS

Tsuyoshi Miezaki, <a href="/A331905/a331905.pdf">A note on spanning trees.</a>

CROSSREFS

Cf. A169630, A331905.

EXTENSIONS

Entry revised by N. J. A. Sloane, Jan 25 2020 and Feb 06 2020.

STATUS

approved

editing

#38 by Bruno Berselli at Tue Jan 28 11:40:34 EST 2020

STATUS

proposed

approved

#37 by Vincenzo Librandi at Tue Jan 28 01:21:41 EST 2020

STATUS

editing

proposed

#36 by Vincenzo Librandi at Tue Jan 28 01:21:18 EST 2020

MATHEMATICA

CoefficientList[Series[x (1 - x^2) (x^4 + x^3 - x^2 + x + 1) / (x^8 - 4 x^6 - x^4 - 4 x^2 + 1), {x, 0, 35}], x] (* Vincenzo Librandi, Jan 28 2020 *)

PROG

(MAGMA) m:=40; R<x>:=PowerSeriesRing(Rationals(), m); [0] cat Coefficients(R!( x*(1-x^2)*(x^4+x^3-x^2+x+1) / (x^8-4*x^6-x^4-4*x^2+1))); // Vincenzo Librandi, Jan 28 2020

STATUS

approved

editing