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A005056 a(n) = 3^n + 2^n - 1. 10

%I

%S 1,4,12,34,96,274,792,2314,6816,20194,60072,179194,535536,1602514,

%T 4799352,14381674,43112256,129271234,387682632,1162785754,3487832976,

%U 10462450354,31385253912,94151567434,282446313696,847322163874,2541932937192,7625731702714

%N a(n) = 3^n + 2^n - 1.

%C Binomial transform of A083313. - _Paul Barry_, Apr 25 2003

%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 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

%H Vincenzo Librandi, <a href="/A005056/b005056.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">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).

%F From _Paul Barry_, Apr 25 2003: (Start)

%F G.f.: (1-2x-x^2)/((1-x)(1-2x)(1-3x)).

%F E.g.f.: exp(3x) + exp(2x) - exp(x). (End)

%F 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

%F 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

%t Table[3^n + 2^n - 1, {n, 0, 60}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 27 2011 *)

%t CoefficientList[Series[(1 - 2 x - x^2) / ((1 - x) (1 - 2 x) (1 - 3 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 08 2013 *)

%o (PARI) a(n) = 3^n + 2^n - 1 \\ _Rick L. Shepherd_, Aug 07 2017

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified September 18 04:14 EDT 2020. Contains 337165 sequences. (Running on oeis4.)