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Number of nonequivalent dissections of a polygon into n quadrilaterals by nonintersecting diagonals rooted at a cell up to rotation.
(Formerly M3921)
3

%I M3921 #27 Aug 20 2019 03:23:53

%S 1,1,5,22,116,612,3399,19228,111041,650325,3856892,23107896,139672312,

%T 850624376,5214734547,32154708216,199292232035,1240877862315,

%U 7758138260565,48685766617950,306558216362064,1936246229757840,12263985131919300,77880114240872112

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

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

%H Andrew Howroyd, <a href="/A005033/b005033.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 T[n_, k_] := DivisorSum[GCD[n-1, k], EulerPhi[#]*u[(n-1)/#, k, k/#]&]/k;

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

%t Array[a, 24] (* _Jean-François Alcover_, Aug 20 2019, after _Andrew Howroyd_ *)

%Y Column k=4 of A295222.

%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