A092880 Number of ordered 2-multiantichains on an n-set.

1, 2, 6, 26, 126, 602, 2766, 12266, 52926, 223802, 932526, 3844106, 15722526, 63936602, 258902286, 1045109546, 4209004926, 16921851002, 67945160046, 272554432586, 1092540156126, 4377129999002, 17529432313806, 70180474597226

Offset

0,2

Comments

Let P(A) be the power set of an n-element set A and R be a relation on P(A) such that for all x, y of P(A), xRy if either 0) x is not a subset of y and y is not a subset of x, or 1) x equals y. Then a(n) = |R|. - Ross La Haye, Mar 19 2009

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.

Index entries for linear recurrences with constant coefficients, signature (9,-26,24).

Formula

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

G.f.: (14*x^2-7*x+1) / ((1-2*x)*(1-3*x)*(1-4*x)). - Colin Barker, Dec 10 2012

Mathematica

Table[4^n - 2*3^n + 2*2^n, {n, 0, 23}] (* Michael De Vlieger, Nov 29 2015 *)

Prog

(PARI) vector(100, n, n--; 4^n - 2*3^n + 2*2^n) \\ Altug Alkan, Nov 29 2015
(Magma) [4^n - 2*3^n + 2*2^n: n in [0..10]]; // G. C. Greubel, Oct 06 2017

Crossrefs

Cf. A092881, A092882, A092883, A092884.

Sequence in context: A358107 A288606 A208034 * A370185 A192808 A034474

Adjacent sequences: A092877 A092878 A092879 * A092881 A092882 A092883

Keyword

nonn,easy

Author

Goran Kilibarda, Vladeta Jovovic, Mar 10 2004

Status

approved