login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005036 Number of ways of dissecting a polygon into n quadrilaterals.
(Formerly M1491)
3

%I M1491

%S 1,1,2,5,16,60,261,1243,6257,32721,175760,963900,5374400,30385256,

%T 173837631,1004867079,5861610475,34469014515,204161960310,

%U 1217145238485,7299007647552,44005602441840

%N Number of ways of dissecting a polygon into n quadrilaterals.

%C The subsequence of primes begins: 2, 5, 6257, no more through a(100). - _Jonathan Vos Post_, Apr 08 2011

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A005036/b005036.txt">Table of n, a(n) for n = 1..100</a>

%H F. Harary, E. M. Palmer and R. C. Read, <a href="http://dx.doi.org/10.1016/0012-365X(75)90041-2">On the cell-growth problem for arbitrary polygons</a>, Discr. Math. 11 (1975), 371-389.

%H E. V. Konstantinova, <a href="http://com2mac.postech.ac.kr/papers/2001/01-06.pdf">A survey of the cell-growth problem and some its variations</a>, Com 2 MaC-KOSEF, 2001.

%H <a href="/index/Cor#core">Index entries for "core" sequences</a>

%t p=4; Table[(Binomial[(p-1)n, n]/(((p-2)n+1)((p-2)n+2)) + If[OddQ[n], If[OddQ[p], Binomial[(p-1)n/2, (n-1)/2]/n, (p+1)Binomial[((p-1)n-1)/2, (n-1)/2]/((p-2)n+2)], 3Binomial[(p-1)n/2, n/2]/((p-2)n+2)]+Plus @@ Map[EulerPhi[ # ]Binomial[((p-1)n+1)/#, (n-1)/# ]/((p-1)n+1)&, Complement[Divisors[GCD[p, n-1]], {1, 2}]])/2, {n, 1, 20}] - _Robert A. Russell_, Dec 11 2004

%Y Cf. A005419, A004127, A005038, A005040, A000207.

%K core,nonn,nice

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _Sascha Kurz_, Oct 13 2001

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 24 16:46 EST 2014. Contains 249899 sequences.