A073020 -id:A073020 - cp's OEIS frontend

A003444 Number of dissections of a polygon.

1, 4, 12, 43, 143, 504, 1768, 6310, 22610, 81752, 297160, 1086601, 3991995, 14732720, 54587280, 202997670, 757398510, 2834510744, 10637507400, 40023636310, 150946230006, 570534578704, 2160865067312, 8199711378716, 31170212479588, 118686578956272

Offset: 4

N. J. A. Sloane

nonn

See A220881 for an essentially identical sequence, but with a different offset and a more precise definition. - N. J. A. Sloane, Dec 28 2012

Also number of necklaces of 2 colors with 2n beads and n-2 black ones. - Wouter Meeussen, Aug 03 2002

P. Lisonek, Closed forms for the number of polygon dissections. Journal of Symbolic Computation 20 (1995), 595-601.
R. C. Read, On general dissections of a polygon, Aequat. Math. 18 (1978), 370-388.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 4..201
D. Bowman and A. Regev, Counting symmetry classes of dissections of a convex regular polygon, arXiv:1209.6270 [math.CO], 2012.

Cf. A003445, A003450, A047996, A073020, A220881.

Table[(Plus@@(EulerPhi[ # ]Binomial[2n/#, (n-2)/# ] &)/@Intersection[Divisors[2n], Divisors[n-2]])/(2n), {n, 3, 32}]

a(n) = (1/(2n)) Sum_{d |(2n, k)} phi(d)*binomial(2n/d, k/d) with k=n-2. - Wouter Meeussen, Aug 03 2002

More terms from Wouter Meeussen, Aug 03 2002

A078925 Triangle of T1(n,m) = number of bracelets (necklaces that can be turned over) with m white beads and (2n+1-m) black ones, for 1<=m<=n.

Original entry on oeis.org

1, 1, 2, 1, 3, 4, 1, 4, 7, 10, 1, 5, 10, 20, 26, 1, 6, 14, 35, 57, 76, 1, 7, 19, 56, 111, 185, 232, 1, 8, 24, 84, 196, 392, 600, 750, 1, 9, 30, 120, 324, 756, 1368, 2052, 2494, 1, 10, 37, 165, 507, 1353, 2829, 4950, 7105, 8524, 1, 11, 44, 220, 759, 2277, 5412, 10824

Offset: 1

Thomas Hartinger (hartinger_t(AT)web.de), Dec 15 2002

Left half of odd rows of table A052307 with left column deleted.

			1; 1, 2; 1, 3, 4; 1, 4, 7, 10; ...

Index entries for sequences related to bracelets

Cf. A052307 for full table, A073020 for even number of beads. Last term in each row gives A007123.

Table[ f[n, 2n + 1], {n, 11}] (* Robert G. Wilson v, Mar 29 2006 *)

cp's OEIS Frontend

A003444 Number of dissections of a polygon.

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