A005419 Number of nonequivalent dissections of a polygon into n heptagons by nonintersecting diagonals up to rotation and reflection. (Formerly M3023)

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

Offset

1,3

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.

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

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 *)

Crossrefs

Column k=7 of A295260.

Sequence in context: A002404 A097142 A039751 * A379193 A332024 A124537

Adjacent sequences: A005416 A005417 A005418 * A005420 A005421 A005422

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Robert A. Russell, Dec 11 2004

Name edited by Andrew Howroyd, Nov 20 2017

Status

approved