A092880 - OEIS

%I #22 Sep 08 2022 08:45:13

%S 1,2,6,26,126,602,2766,12266,52926,223802,932526,3844106,15722526,

%T 63936602,258902286,1045109546,4209004926,16921851002,67945160046,

%U 272554432586,1092540156126,4377129999002,17529432313806,70180474597226

%N Number of ordered 2-multiantichains on an n-set.

%C 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

%H G. C. Greubel, <a href="/A092880/b092880.txt">Table of n, a(n) for n = 0..1000</a>

%H Ross La Haye, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/LaHaye/lahaye5.html">Binary Relations on the Power Set of an n-Element Set</a>, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-26,24).

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

%F G.f.: (14*x^2-7*x+1) / ((1-2*x)*(1-3*x)*(1-4*x)). - _Colin Barker_, Dec 10 2012

%t Table[4^n - 2*3^n + 2*2^n, {n, 0, 23}] (* _Michael De Vlieger_, Nov 29 2015 *)

%o (PARI) vector(100, n, n--; 4^n - 2*3^n + 2*2^n) \\ _Altug Alkan_, Nov 29 2015

%o (Magma) [4^n - 2*3^n + 2*2^n: n in [0..10]]; // _G. C. Greubel_, Oct 06 2017

%Y Cf. A092881, A092882, A092883, A092884.

%K nonn,easy

%O 0,2

%A Goran Kilibarda, _Vladeta Jovovic_, Mar 10 2004