OFFSET
0,2
COMMENTS
Binomial transform of A083313. - Paul Barry, Apr 25 2003
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 a proper subset of y or y is a proper subset of x and x and y are disjoint, 1) x is not a subset of y and y is not a subset of x and x and y are disjoint, or 2) x equals y. Then a(n) = |R|. - Ross La Haye, Mar 19 2009
LINKS
Vincenzo Librandi, 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 (6,-11,6).
FORMULA
From Paul Barry, Apr 25 2003: (Start)
G.f.: (1-2x-x^2)/((1-x)(1-2x)(1-3x)).
E.g.f.: exp(3x) + exp(2x) - exp(x). (End)
a(n) = 5*a(n-1) - 6*a(n-2) - 2 for n > 1, a(0)=1, a(1)=4. - Vincenzo Librandi, Dec 31 2010
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n > 2, a(0)=1, a(1)=4, a(2)=12. - Rick L. Shepherd, Aug 07 2017
a(n) = A007689(n)-1. - R. J. Mathar, Mar 10 2022
MATHEMATICA
Table[3^n + 2^n - 1, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Jun 27 2011 *)
CoefficientList[Series[(1 - 2 x - x^2) / ((1 - x) (1 - 2 x) (1 - 3 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 08 2013 *)
LinearRecurrence[{6, -11, 6}, {1, 4, 12}, 30] (* Harvey P. Dale, Aug 18 2023 *)
PROG
(PARI) a(n) = 3^n + 2^n - 1 \\ Rick L. Shepherd, Aug 07 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved