login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A295622 Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals rooted at a cell up to rotation. 2
3, 11, 24, 46, 75, 117, 168, 236, 315, 415, 528, 666, 819, 1001, 1200, 1432, 1683, 1971, 2280, 2630, 3003, 3421, 3864, 4356, 4875, 5447, 6048, 6706, 7395, 8145, 8928, 9776, 10659, 11611, 12600, 13662, 14763, 15941, 17160, 18460, 19803, 21231, 22704, 24266 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,1

LINKS

Andrew Howroyd, Table of n, a(n) for n = 5..500

P. Lisonek, Closed forms for the number of polygon dissections, Journal of Symbolic Computation 20 (1995), 595-601.

C. R. Read, On general dissections of a polygon, Aequat. math. 18 (1978) 370-388.

FORMULA

Conjectures from Colin Barker, Nov 25 2017: (Start)

G.f.: x^5*(3 + 5*x - x^2 - x^3) / ((1 - x)^4*(1 + x)^2).

a(n) = (n-4)*(-5 + (-1)^n - 4*n + 2*n^2) / 8 for n>4.

a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>10.

(End)

a(n) = Sum_{k=0..n-5} f(k), where f(n) = Sum_{k=0..n} 3 + lcm(k, 2)) (conjecture). - Jon Maiga, Nov 28 2018

MAPLE

seq(coeff(series((3+5*x-x^2-x^3)/((x-1)^4*(x+1)^2), x, n+1), x, n), n = 0 .. 45); # Muniru A Asiru, Nov 28 2018

MATHEMATICA

f[n_] := (n - 4)*(2n^2 - 4n - 5 + (-1)^n)/8; Array[f, 44, 5] (* or *)

LinearRecurrence[{2, 1, -4, 1, 2, -1}, {3, 11, 24, 46, 75, 117}, 44] (* or *)

CoefficientList[ Series[-(x^3 + x^2 - 5x - 3)/((x - 1)^4 (x + 1)^2), {x, 0, 43}], x] (* Robert G. Wilson v, Nov 25 2017 *)

PROG

(PARI) \\ See A003442 for DissectionsModCyclicRooted()

{ my(v=DissectionsModCyclicRooted(apply(i->y + O(y^4), [1..40]))); apply(p->polcoeff(p, 3), v[5..#v]) }

CROSSREFS

Cf. A003442, A003451, A003452, A003453.

Sequence in context: A293404 A293414 A212252 * A294415 A141595 A112051

Adjacent sequences:  A295619 A295620 A295621 * A295623 A295624 A295625

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Nov 24 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)