A005419 Number of nonequivalent dissections of a polygon into n heptagons by nonintersecting diagonals up to rotation and reflection.

1, 1, 3, 16, 112, 1020, 10222, 109947, 1230840, 14218671, 168256840, 2031152928, 24931793768, 310420597116, 3912823963482, 49853370677834, 641218583442360, 8316918403772790, 108686334145327785, 1429927553582849256, 18927697628428129728, 251931892228273729375

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..850
• F. Harary, E. M. Palmer and R. C. Read, On the cell-growth problem for arbitrary polygons, Discr. Math. 11 (1975), 371-389.

Crossrefs

Column k=7 of A295260.

Programs

Mathematica

p=7; 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 *)

Formula

See Mathematica code.

a(n) ~ 2^(6*n - 1) * 3^(6*n + 1/2) / (sqrt(Pi) * n^(5/2) * 5^(5*n + 5/2)). - Vaclav Kotesovec, Mar 13 2016

Extensions

More terms from Robert A. Russell, Dec 11 2004

Name edited by Andrew Howroyd, Nov 20 2017