A094729 Number of connected ordered 2-element multiantichains on a labeled n-set.

0, 1, 1, 7, 37, 151, 541, 1807, 5797, 18151, 55981, 171007, 519157, 1569751, 4733821, 14250607, 42850117, 128746951, 386634061, 1160688607, 3483638677, 10454061751, 31368476701, 94118013007, 282379204837, 847187946151, 2541664501741, 7625194831807

Offset: 0

Author

Goran Kilibarda, Vladeta Jovovic, May 24 2004

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

Crossrefs

Cf. A094033-A094037, A094729-A094738.

Programs

Mathematica

With[{nmax = 50}, CoefficientList[Series[Exp[3*x] - 3*Exp[2*x] + 4*Exp[x] - 2, {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Oct 06 2017 *)
LinearRecurrence[{6,-11,6},{0,1,1,7},30] (* Harvey P. Dale, Aug 07 2023 *)

PARI

x='x+O('x^50); concat([0], Vec(serlaplace(exp(3*x)-3*exp(2*x) +4*exp(x)-2))) \\ G. C. Greubel, Oct 06 2017

PARI

concat(0, Vec(x*(1 - 5*x + 12*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)) + O(x^30))) \\ Colin Barker, Oct 13 2017

Formula

E.g.f.: exp(3*x) - 3*exp(2*x) + 4*exp(x) - 2.

From Colin Barker, Jul 07 2013: (Start)

a(n) = 4-3*2^n+3^n for n>0.

a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3) for n>3.

G.f.: x*(1 - 5*x + 12*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).

(End)