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 A091344 a(n) = 2*3^n - 3*2^n + 1. 10
 0, 1, 7, 31, 115, 391, 1267, 3991, 12355, 37831, 115027, 348151, 1050595, 3164071, 9516787, 28599511, 85896835, 257887111, 774054547, 2322950071, 6970423075, 20914414951, 62749536307, 188261191831, 564808741315, 1694476555591 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Starting with offset 1 = binomial transform of A068193: (1, 6, 18, 42, 90, ...) and double binomial transform of (1, 5, 7, 5, 7, 5, ...). - Gary W. Adamson, Jan 13 2009 Number of pairs (A,B) where A and B are nonempty subsets of {1,2,...,n} and one of these subsets is a subset of the other. - For the case that one of these subsets is a proper subset of the other see a(n+1) in A260217. - If empty subsets are included, see A027649 (all subsets) and A056182 (proper subsets). - Manfred Boergens, Aug 02 2023 LINKS Table of n, a(n) for n=0..25. Christian Ballot and Florian Luca, Prime factors of a^f(n)-1 with an irreducible polynomial f(x),New York J. Math. 12 (2006), 39-45 (electronic). Christian Ballot and Florian Luca, Common prime factors of a^n-b and c^n-d, Unif. Distrib. Theory 2 (2007), no. 2, 19-34 (electronic). John Elias, Illustration of initial terms: Sixfold Sierpinski Stars Index entries for linear recurrences with constant coefficients, signature (6,-11,6). FORMULA a(n) = Sum_{i=1..n} i!*i^2*Stirling2(n,i)*(-1)^(n-i). From Christian Ballot via R. K. Guy, Jan 13 2009: (Start) a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3); G.f.: x*(1+x)/((1-x)*(2-x)*(3-x)). (End) a(n) = 5*a(n-1) - 6*a(n-2) + 2, a(0)=0, a(1)=1. - Vincenzo Librandi, Nov 25 2010 MAPLE a:=n->sum((3^(n-j-1)-2^(n-2-j))*12, j=0..n): seq(a(n), n=-1..24); # Zerinvary Lajos, Feb 11 2007 with (combinat):a:=n->stirling2(n, 3)+stirling2(n+1, 3): seq(a(n), n=1..26); # Zerinvary Lajos, Oct 07 2007 MATHEMATICA Table[Sum[i!i^2 StirlingS2[n, i](-1)^(n - i), {i, 1, n}], {n, 0, 30}] Table[2*3^n-3*2^n+1, {n, 0, 30}] (* or *) LinearRecurrence[{6, -11, 6}, {0, 1, 7}, 30] (* Harvey P. Dale, Dec 31 2013 *) CROSSREFS Cf. A068293. - Gary W. Adamson, Jan 13 2009 Cf. A027649, A056182, A260217. Sequence in context: A350498 A197649 A006458 * A032197 A114289 A147597 Adjacent sequences: A091341 A091342 A091343 * A091345 A091346 A091347 KEYWORD easy,nonn AUTHOR Mario Catalani (mario.catalani(AT)unito.it), Jan 01 2004 EXTENSIONS Edited by N. J. A. Sloane, Jan 13 2009 at the suggestion of R. K. Guy; the concise definition was provided by Vladeta Jovovic, Jan 01 2004 STATUS approved

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Last modified February 24 20:15 EST 2024. Contains 370307 sequences. (Running on oeis4.)