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
KEYWORD
nonn,easy
AUTHOR
Martin Griffiths, Dec 01 2009
STATUS
approved