A005033 Number of nonequivalent dissections of a polygon into n quadrilaterals by nonintersecting diagonals rooted at a cell up to rotation.

1, 1, 5, 22, 116, 612, 3399, 19228, 111041, 650325, 3856892, 23107896, 139672312, 850624376, 5214734547, 32154708216, 199292232035, 1240877862315, 7758138260565, 48685766617950, 306558216362064, 1936246229757840, 12263985131919300, 77880114240872112

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=4 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, 4];
Array[a, 24] (* 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