%I M3471 #27 Jul 02 2018 08:04:27

%S 1,1,4,13,64,315,1727,9658,55657,325390,1929160,11555172,69840032,

%T 425318971,2607388905,16077392564,99646239355,620439153165,

%U 3879069845640,24342884609625,153279112388352,968123122592340,6131992590993204,38940057166651848

%N Number of nonequivalent dissections of a polygon into n quadrilaterals by nonintersecting diagonals rooted at a cell up to rotation and reflection.

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

%H Andrew Howroyd, <a href="/A005035/b005035.txt">Table of n, a(n) for n = 1..200</a>

%H F. Harary, E. M. Palmer, R. C. Read, <a href="/A000108/a000108_20.pdf">On the cell-growth problem for arbitrary polygons, computer printout, circa 1974</a>

%H F. Harary, E. M. Palmer and R. C. Read, <a href="http://dx.doi.org/10.1016/0012-365X(75)90041-2">On the cell-growth problem for arbitrary polygons</a>, Discr. Math. 11 (1975), 371-389.

%t u[n_, k_, r_] := r*Binomial[(k-1)*n + r, n]/((k-1)*n + r);

%t F[n_, k_] := DivisorSum[GCD[n-1, k], EulerPhi[#]*u[(n-1)/#, k, k/#]&]/k;

%t 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;

%t a[n_] := T[n, 4];

%t Array[a, 24] (* _Jean-François Alcover_, Jul 02 2018, after _Andrew Howroyd_ *)

%Y Column k=4 of A295259.

%K nonn

%O 1,3

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Mar 11 2016

%E Name edited by _Andrew Howroyd_, Nov 20 2017