This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A005056 #38 Aug 18 2023 10:40:35
%S A005056 1,4,12,34,96,274,792,2314,6816,20194,60072,179194,535536,1602514,
%T A005056 4799352,14381674,43112256,129271234,387682632,1162785754,3487832976,
%U A005056 10462450354,31385253912,94151567434,282446313696,847322163874,2541932937192,7625731702714
%N A005056 a(n) = 3^n + 2^n - 1.
%C A005056 Binomial transform of A083313. - _Paul Barry_, Apr 25 2003
%C A005056 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 A005056 Vincenzo Librandi, <a href="/A005056/b005056.txt">Table of n, a(n) for n = 0..1000</a>
%H A005056 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 A005056 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F A005056 From _Paul Barry_, Apr 25 2003: (Start)
%F A005056 G.f.: (1-2x-x^2)/((1-x)(1-2x)(1-3x)).
%F A005056 E.g.f.: exp(3x) + exp(2x) - exp(x). (End)
%F A005056 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 A005056 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
%F A005056 a(n) = A007689(n)-1. - _R. J. Mathar_, Mar 10 2022
%t A005056 Table[3^n + 2^n - 1, {n, 0, 60}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 27 2011 *)
%t A005056 CoefficientList[Series[(1 - 2 x - x^2) / ((1 - x) (1 - 2 x) (1 - 3 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 08 2013 *)
%t A005056 LinearRecurrence[{6,-11,6},{1,4,12},30] (* _Harvey P. Dale_, Aug 18 2023 *)
%o A005056 (PARI) a(n) = 3^n + 2^n - 1 \\ _Rick L. Shepherd_, Aug 07 2017
%Y A005056 Cf. A083313.
%K A005056 nonn,easy
%O A005056 0,2
%A A005056 _N. J. A. Sloane_