A005037 - OEIS

A005037

Number of nonequivalent dissections of a polygon into n pentagons by nonintersecting diagonals rooted at a cell up to rotation.
(Formerly M4236)

1, 1, 6, 40, 285, 2126, 16380, 129456, 1043460, 8544965, 70893054, 594610536, 5033644070, 42952562100, 369061673400, 3190379997272, 27727712947836, 242135589539124, 2123541227823800, 18695484623015200, 165169213716082765

(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);

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

a[n_] := T[n, 5];

Array[a, 21] (* Jean-François Alcover, Aug 20 2019, after Andrew Howroyd *)

CROSSREFS

Column k=5 of A295222.

Sequence in context: A178397 A090041 A069720 * A081337 A316912 A366199

Adjacent sequences: A005034 A005035 A005036 * A005038 A005039 A005040

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