OFFSET
0,2
COMMENTS
A082134 is the analogous sequence if "union" is replaced by "intersection" and A002697 is the analogous sequence if "union" is replaced by "symmetric difference". Here, X union Y = Y union X are considered as the same Cartesian product [Relation (37): U_Q(n) in document of Ross La Haye in reference], if we want to consider that X Union Y and Y Union X are two distinct Cartesian products, see A212698. [Bernard Schott, Jan 11 2013]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
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 (12,-52,96,-64).
FORMULA
a(n) = n*(2^(n-2) + 3*2^(2*n-3)).
G.f.: 2*x*(7*x^2-5*x+1) / ((2*x-1)^2*(4*x-1)^2). [Colin Barker, Dec 10 2012]
E.g.f.: exp(2*x)*(1 + 3*exp(2*x))*x. - Stefano Spezia, Aug 04 2022
EXAMPLE
a(2) = 14 because for P(A) = {{},{1},{2},{1,2}} |{} union {1}| = 1, |{} union {2}| = 1, |{} union {1,2}| = 2, |{1} union {2}| = 2, |{1} union {1,2}| = 2 and |{2} union {1,2}| = 2, |{} union {}| = 0, |{1} union {1}| = 1, |{2} union {2}| = 1, |{1,2} union {1,2}| = 2, which sums to 14.
MATHEMATICA
LinearRecurrence[{12, -52, 96, -64}, {0, 2, 14, 78}, 30] (* Harvey P. Dale, Jan 24 2019 *)
PROG
(Magma) [n*(2^(n-2) + 3*2^(2*n-3)): n in [0..30]]; // Vincenzo Librandi, Jun 10 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ross La Haye, Dec 30 2007, Jan 03 2008
STATUS
approved