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 A005039 Number of nonequivalent dissections of a polygon into n pentagons by nonintersecting diagonals rooted at a cell up to rotation and reflection. (Formerly M3589) 3
 1, 1, 4, 22, 147, 1074, 8216, 64798, 521900, 4272967, 35447724, 297308810, 2516830890, 21476307960, 184530904560, 1595190209002, 13863857007924, 121067796450692, 1061770618201680, 9347742325179544, 82584606893075739 (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 Vaclav Kotesovec, Table of n, a(n) for n = 1..1000 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. FORMULA G.f.: (1/10)*x*(u^5(x) + 4*u(x^5) + 5*u^2(x^2) + 5*x*u^4(x^2)) where u(x) is the g.f. for A002293. - Sean A. Irvine, Mar 12 2016 a(n) ~ 2^(8*n - 1/2) / (sqrt(Pi) * n^(3/2) * 3^(3*n + 5/2)). - Vaclav Kotesovec, Mar 13 2016 MATHEMATICA Rest[CoefficientList[Series[x*(HypergeometricPFQ[{1/4, 1/2, 3/4}, {2/3, 4/3}, (256/27)*x]^5 + 4*HypergeometricPFQ[{1/4, 1/2, 3/4}, {2/3, 4/3}, (256/27)*x^5] + 5*HypergeometricPFQ[{1/4, 1/2, 3/4}, {2/3, 4/3}, (256/27)*x^2]^2 + 5*x*HypergeometricPFQ[{1/4, 1/2, 3/4}, {2/3, 4/3}, (256/27)*x^2]^4)/10, {x, 0, 25}], x]] (* Vaclav Kotesovec, Mar 13 2016 *) CROSSREFS Column k=5 of A295259. Cf. A002293, A005037 (no mirror-image symmetries), A003446 (triangles), A005035 (quadrilaterals). Sequence in context: A196795 A278396 A121394 * A199418 A112898 A253095 Adjacent sequences:  A005036 A005037 A005038 * A005040 A005041 A005042 KEYWORD nonn AUTHOR EXTENSIONS More terms from Sean A. Irvine, Mar 12 2016 Name edited by Andrew Howroyd, Nov 20 2017 STATUS approved

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Last modified June 24 01:22 EDT 2018. Contains 311819 sequences. (Running on oeis4.)