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A033276 Number of diagonal dissections of an n-gon into 4 regions. 6
0, 14, 84, 300, 825, 1925, 4004, 7644, 13650, 23100, 37400, 58344, 88179, 129675, 186200, 261800, 361284, 490314, 655500, 864500, 1126125, 1450449, 1848924, 2334500, 2921750, 3627000, 4468464, 5466384, 6643175, 8023575, 9634800, 11506704, 13671944 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

COMMENTS

Number of standard tableaux of shape (n-4,2,2,2) (n>=6). - Emeric Deutsch, May 20 2004

Number of short bushes with n+2 edges and 4 branch nodes (i.e. nodes with outdegree at least 2). A short bush is an ordered tree with no nodes of outdegree 1. Example: a(6)=14 because the only short bushes with 8 edges and 4 branch nodes are the fourteen full binary trees with 8 edges. Column 4 of A108263. - Emeric Deutsch, May 29 2005

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 5..1000

D. Beckwith, Legendre polynomials and polygon dissections?, Amer. Math. Monthly, 105 (1998), 256-257.

F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discr. Math., 204 (1999) 73-112.

C. R. Read, On general dissections of a polygon, Aequat. math. 18 (1978) 370-388, Table 1.

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

FORMULA

a(n) = binomial(n+2, 3)*binomial(n-3, 3)/4.

G.f.: z^6(14-14z+6z^2-z^3)/(1-z)^7. - Emeric Deutsch, May 29 2005

MATHEMATICA

Table[(Binomial[n+2, 3]Binomial[n-3, 3])/4, {n, 5, 40}] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {0, 14, 84, 300, 825, 1925, 4004}, 40] (* Harvey P. Dale, Mar 13 2014 *)

CoefficientList[Series[x (14 - 14 x + 6 x^2 - x^3)/(1 - x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 15 2014 *)

PROG

(MAGMA) [(Binomial(n+2, 3)*Binomial(n-3, 3))/4: n in [5..50]]; // Vincenzo Librandi, Mar 15 2014

CROSSREFS

Cf. A033275, A108263.

Sequence in context: A085036 A107935 A008451 * A006858 A027818 A054149

Adjacent sequences:  A033273 A033274 A033275 * A033277 A033278 A033279

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Mar 15 2014

STATUS

approved

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Last modified October 18 05:17 EDT 2018. Contains 316304 sequences. (Running on oeis4.)