login
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
OFFSET
1,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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: A278396 A369617 A121394 * A199418 A112898 A368733
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Mar 12 2016
Name edited by Andrew Howroyd, Nov 20 2017
STATUS
approved