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A005035
Number of nonequivalent dissections of a polygon into n quadrilaterals by nonintersecting diagonals rooted at a cell up to rotation and reflection.
(Formerly M3471)
4
1, 1, 4, 13, 64, 315, 1727, 9658, 55657, 325390, 1929160, 11555172, 69840032, 425318971, 2607388905, 16077392564, 99646239355, 620439153165, 3879069845640, 24342884609625, 153279112388352, 968123122592340, 6131992590993204, 38940057166651848
OFFSET
1,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
F. Harary, E. M. Palmer and R. C. Read, On the cell-growth problem for arbitrary polygons, Discr. Math. 11 (1975), 371-389.
MATHEMATICA
u[n_, k_, r_] := r*Binomial[(k-1)*n + r, n]/((k-1)*n + r);
F[n_, k_] := DivisorSum[GCD[n-1, k], EulerPhi[#]*u[(n-1)/#, k, k/#]&]/k;
T[n_, k_] := (F[n, k] + If[OddQ[k], If[OddQ[n], u[(n-1)/2, k, (k-1)/2], u[n/2-1, k, k-1]], If[OddQ[n], u[(n-1)/2, k, k/2+1], u[n/2-1, k, k]]])/2;
a[n_] := T[n, 4];
Array[a, 24] (* Jean-François Alcover, Jul 02 2018, after Andrew Howroyd *)
CROSSREFS
Column k=4 of A295259.
Sequence in context: A135312 A287145 A266096 * A340452 A222771 A052415
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Mar 11 2016
Name edited by Andrew Howroyd, Nov 20 2017
STATUS
approved