The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A005035

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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.
(history; published version)

#27 by Alois P. Heinz at Mon Jul 02 08:04:27 EDT 2018

STATUS

proposed

approved

#26 by Jean-François Alcover at Mon Jul 02 07:56:47 EDT 2018

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editing

proposed

#25 by Jean-François Alcover at Mon Jul 02 07:56:43 EDT 2018

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 *)

STATUS

approved

editing

#24 by Joerg Arndt at Wed Jan 17 11:40:53 EST 2018

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reviewed

approved

#23 by Michel Marcus at Wed Jan 17 11:40:15 EST 2018

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proposed

reviewed

#22 by Rachel Barnett at Wed Jan 17 11:36:32 EST 2018

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editing

proposed

#21 by Rachel Barnett at Wed Jan 17 11:36:29 EST 2018

LINKS

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>

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approved

editing

#20 by Susanna Cuyler at Mon Nov 20 22:05:44 EST 2017

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proposed

approved

#19 by Jon E. Schoenfield at Mon Nov 20 20:46:58 EST 2017

STATUS

editing

proposed

#18 by Jon E. Schoenfield at Mon Nov 20 20:46:51 EST 2017

AUTHOR

N. J. A. Sloane.

STATUS

proposed

editing