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 A094374 a(n)=(3^n-1)/2+2^n. 4
 1, 3, 8, 21, 56, 153, 428, 1221, 3536, 10353, 30548, 90621, 269816, 805353, 2407868, 7207221, 21588896, 64701153, 193972388, 581655021, 1744440776, 5232273753, 15694724108, 47079978021, 141231545456, 423677859153, 1271000023028, 3812932960221, 11438664662936 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A094373. Row sums of A125103. - Paul Barry, Dec 04 2007 Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are disjoint and for which either x is a subset of y or y is a subset of x, or 1) x and y are disjoint and for which x is not a subset of y and y is not a subset of x, or 2) x = y. - Ross La Haye, Jan 11 2008 LINKS 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. A. Prasad, Equivalence classes of nodes in trees and rational generating functions, arXiv preprint arXiv:1407.5284 [math.CO], 2014. Index entries for linear recurrences with constant coefficients, signature (6,-11,6). FORMULA G.f.: (1-3x+x^2)/((1-x)(1-2x)(1-3x)). a(n) = 6a(n-1)-11a(n-2)+6a(n-3). a(n) = A003462(n)+A000079(n). a(n) = sum{k=0..n, C(n,k)+2^k*C(n,k+1)}; - Paul Barry, Dec 04 2007 a(n) = StirlingS2(n+1,3) + 2*StirlingS2(n+1,2) + 1. - Ross La Haye, Jan 11 2008 a(0)=1, a(1)=3, a(2)=8, a(n)=6*a(n-1)-11*a(n-2)+6*a(n-3). - Harvey P. Dale, Jul 22 2013 MATHEMATICA Table[(3^n-1)/2+2^n, {n, 0, 30}] (* or *) LinearRecurrence[{6, -11, 6}, {1, 3, 8}, 30] (* Harvey P. Dale, Jul 22 2013 *) PROG (PARI) a(n)=(3^n-1)/2+2^n \\ Charles R Greathouse IV, Oct 16 2015 (MAGMA) [(3^n-1)/2+2^n: n in [0..30]]; // Vincenzo Librandi, Nov 30 2015 CROSSREFS Cf. A000225, A000392, A000079. Sequence in context: A128105 A085560 A243633 * A008909 A006835 A014318 Adjacent sequences:  A094371 A094372 A094373 * A094375 A094376 A094377 KEYWORD easy,nonn,changed AUTHOR Paul Barry, Apr 28 2004 STATUS approved

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