The On-Line Encyclopedia of Integer Sequences (OEIS)

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A002056

Number of diagonal dissections of a convex n-gon into n-5 regions.
(history; published version)

#70 by Charles R Greathouse IV at Thu Sep 08 08:44:29 EDT 2022

PROG

(MAGMAMagma) [Binomial(n-3, 3)*Binomial(2*n-7, n-6)/(n-5): n in [6..30]]; // Vincenzo Librandi, Feb 18 2020

Discussion

Thu Sep 08

08:44

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

#69 by Charles R Greathouse IV at Wed Apr 13 13:25:16 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

#68 by Charles R Greathouse IV at Fri Mar 12 22:32:35 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

#67 by N. J. A. Sloane at Mon Feb 22 12:12:20 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

#66 by N. J. A. Sloane at Tue Jan 19 11:48:00 EST 2021

LINKS

Ronald C. R. Read, <a href="http://dx.doi.org/10.1007/BF03031688">On general dissections of a polygon</a>, Aequat. math. 18 (1978) 370-388, Table 1.

Discussion

Tue Jan 19

11:48

OEIS Server: https://oeis.org/edit/global/2884

#65 by Alois P. Heinz at Tue Feb 18 07:23:59 EST 2020

STATUS

proposed

approved

#64 by Michel Marcus at Tue Feb 18 02:02:03 EST 2020

STATUS

editing

proposed

#63 by Michel Marcus at Tue Feb 18 02:01:57 EST 2020

COMMENTS

a(n) = number Number of noncrossing partitions of 2n-7 into n-5 blocks all of size at least 2. - Oliver Pechenik, May 02 2014

LINKS

A. Cayley, <a href="httphttps://doi.org/10.1112/plms.oxfordjournals.org/content/s1-22/.1/.237.extract">On the partitions of a polygon</a>, Proc. London Math. Soc., 22 (1891), 237-262 = Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 13, pp. 93ff.

Simon Plouffe, <a href="https://arxiv.org/abs/0912.0072"> Une méthode pour obtenir la fonction génératrice d'une série</a>. , FPSAC 1993, Florence. Formal Power Series and Algebraic Combinatorics; arXiv:0912.0072 [math.NT], 2009.

R. C. Read, <a href="/A001004/a001004.pdf">On general dissections of a polygon</a>, Preprint (1974).

STATUS

proposed

editing

#62 by Vincenzo Librandi at Tue Feb 18 01:56:06 EST 2020

STATUS

editing

proposed

#61 by Vincenzo Librandi at Tue Feb 18 01:55:47 EST 2020

DATA

1, 14, 120, 825, 5005, 28028, 148512, 755820, 3730650, 17978180, 84987760, 395482815, 1816357725, 8250123000, 37119350400, 165645101160, 733919156190, 3231337461300, 14147884842000, 61636377252450, 267325773340626, 1154761882042824, 4969989654817600

PROG

(MAGMA) [Binomial(n-3, 3)*Binomial(2*n-7, n-6)/(n-5): n in [6..30]]; // Vincenzo Librandi, Feb 18 2020

STATUS

approved

editing