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
KEYWORD
nonn,easy
AUTHOR
Goran Kilibarda, Vladeta Jovovic, Mar 10 2004
STATUS
approved