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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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.

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-Fran├žois Alcover, Jul 02 2018, after Andrew Howroyd *)

CROSSREFS

Column k=4 of A295259.

Sequence in context: A135312 A287145 A266096 * A222771 A052415 A129433

Adjacent sequences:  A005032 A005033 A005034 * A005036 A005037 A005038

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Sean A. Irvine, Mar 11 2016

Name edited by Andrew Howroyd, Nov 20 2017

STATUS

approved

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Last modified March 18 19:58 EDT 2019. Contains 321293 sequences. (Running on oeis4.)