A005037 Number of nonequivalent dissections of a polygon into n pentagons by nonintersecting diagonals rooted at a cell up to rotation.

1, 1, 6, 40, 285, 2126, 16380, 129456, 1043460, 8544965, 70893054, 594610536, 5033644070, 42952562100, 369061673400, 3190379997272, 27727712947836, 242135589539124, 2123541227823800, 18695484623015200, 165169213716082765

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

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• F. Harary, E. M. Palmer, R. C. Read, On the cell-growth problem for arbitrary polygons, computer printout, circa 1974
• 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=5 of A295222.

Programs

Mathematica

u[n_, k_, r_] := r*Binomial[(k-1)*n + r, n]/((k-1)*n + r);
T[n_, k_] := DivisorSum[GCD[n-1, k], EulerPhi[#]*u[(n-1)/#, k, k/#]&]/k;
a[n_] := T[n, 5];
Array[a, 21] (* Jean-François Alcover, Aug 20 2019, after Andrew Howroyd *)

Extensions

More terms from Sean A. Irvine, Mar 11 2016

Name edited by Andrew Howroyd, Nov 20 2017