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

%I A005033 M3921 #27 Aug 20 2019 03:23:53
%S A005033 1,1,5,22,116,612,3399,19228,111041,650325,3856892,23107896,139672312,
%T A005033 850624376,5214734547,32154708216,199292232035,1240877862315,
%U A005033 7758138260565,48685766617950,306558216362064,1936246229757840,12263985131919300,77880114240872112
%N A005033 Number of nonequivalent dissections of a polygon into n quadrilaterals by nonintersecting diagonals rooted at a cell up to rotation.
%D A005033 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005033 Andrew Howroyd, <a href="/A005033/b005033.txt">Table of n, a(n) for n = 1..200</a>
%H A005033 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 A005033 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 A005033 u[n_, k_, r_] := r*Binomial[(k-1)*n + r, n]/((k-1)*n + r);
%t A005033 T[n_, k_] := DivisorSum[GCD[n-1, k], EulerPhi[#]*u[(n-1)/#, k, k/#]&]/k;
%t A005033 a[n_] := T[n, 4];
%t A005033 Array[a, 24] (* _Jean-François Alcover_, Aug 20 2019, after _Andrew Howroyd_ *)
%Y A005033 Column k=4 of A295222.
%K A005033 nonn
%O A005033 1,3
%A A005033 _N. J. A. Sloane_
%E A005033 More terms from _Sean A. Irvine_, Mar 11 2016
%E A005033 Name edited by _Andrew Howroyd_, Nov 20 2017