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 A168604 a(n) = 2^(n-2) - 1. 11
 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647, 4294967295, 8589934591 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 COMMENTS Number of ways of partitioning the multiset {1,1,1,2,3,...,n-2} into exactly two nonempty parts. An elephant sequence, see A175655. For the central square six A[5] vectors, with decimal values between 26 and 176, lead to this sequence. For the corner squares these vectors lead to the companion sequence A000325 (without the first leading 1). - Johannes W. Meijer, Aug 15 2010 LINKS Vincenzo Librandi, Table of n, a(n) for n = 3..1000 M. Griffiths, I. Mezo, A generalization of Stirling Numbers of the Second Kind via a special multiset, JIS 13 (2010) #10.2.5 Index entries for linear recurrences with constant coefficients, signature (3,-2). FORMULA E.g.f.: 2*exp(2*x)-exp(x). a(n) = A000225(n-2). G.f.: x^3/((1-x)*(1-2*x)) a(n) = A126646(n-3). - R. J. Mathar, Dec 11 2009 a(n) = 3*a(n-1) - 2*a(n-2). - Arkadiusz Wesolowski, Jun 14 2013 a(n) = A000918(n-2) + 1. - Miquel Cerda, Aug 09 2016 EXAMPLE The partitions of {1,1,1,2,3} into exactly two nonempty parts are {{1},{1,1,2,3}}, {{2},{1,1,1,3}}, {{3},{1,1,1,2}}, {{1,1},{1,2,3}}, {{1,2},{1,1,3}}, {{1,3},{1,1,2}} and {{2,3},{1,1,1}}. MATHEMATICA f4[n_] := 2^(n - 2) - 1; Table[f4[n], {n, 3, 30}] LinearRecurrence[{3, -2}, {1, 3}, 40] (* Harvey P. Dale, Oct 20 2013 *) PROG (MAGMA) [2^(n-2)-1 : n in [3..35]]; // Vincenzo Librandi, May 13 2011 (PARI) a(n)=2^(n-2)-1 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS The number of ways of partitioning the multiset {1, 1, 1, 2, 3, ..., n-1} into exactly three and four nonempty parts are given in A168605 and A168606, respectively. Sequence in context: A000225 A225883 A255047 * A123121 A117060 A178460 Adjacent sequences:  A168601 A168602 A168603 * A168605 A168606 A168607 KEYWORD nonn,easy AUTHOR Martin Griffiths, Dec 01 2009 STATUS approved

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Last modified October 15 05:43 EDT 2019. Contains 328026 sequences. (Running on oeis4.)