A232492 Number of symmetry classes of 3-eared triangulations of an n-gon.

0, 1, 1, 5, 14, 42, 112, 304, 768, 1928, 4696, 11280, 26624, 62160, 143360, 327744, 742752, 1671296, 3735552, 8301504, 18350080, 40370688, 88429952, 192939008, 419430400, 908768000, 1962934272, 4227862528, 9082066432, 19461578752, 41607495680, 88762674176, 188978561024, 401579474944

Offset

5,4

Links

Table of n, a(n) for n=5..38.

A. Regev, Remarks on two-eared triangulations, arXiv preprint arXiv:1309.0743 [math.CO], 2013-2014.

Index entries for linear recurrences with constant coefficients, signature (6,-10,-2,12,4,8,-48,32).

Formula

See Maple code.

G.f.: -x^6*(1-5*x+9*x^2-4*x^3-2*x^4+8*x^6-6*x^5) / ( (2*x^2-1)*(2*x^3-1)*(2*x-1)^3 ). - R. J. Mathar, Dec 04 2013

Maple

f:=proc(n) local t1;
t1:=2^(n-8)*(n-4)*(n-5)/3;
if (n mod 2) = 0 then t1:=t1+2^(n/2-4); fi;
if (n mod 3) = 0 then t1:=t1+2^(n/3-2)/3; fi;
t1; end; [seq(f(n), n=5..50)];

Mathematica

LinearRecurrence[{6, -10, -2, 12, 4, 8, -48, 32}, {0, 1, 1, 5, 14, 42, 112, 304}, 40] (* Jean-François Alcover, Dec 06 2017 *)

Crossrefs

Cf. A005418.

Sequence in context: A147978 A266941 A034549 * A180774 A210972 A197607

Adjacent sequences: A232489 A232490 A232491 * A232493 A232494 A232495

Keyword

nonn

Author

N. J. A. Sloane, Dec 02 2013

Status

approved