login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A168583 The number of ways of partitioning the multiset {1,1,2,3,...,n-1} into exactly three nonempty parts. 5
1, 4, 16, 58, 196, 634, 1996, 6178, 18916, 57514, 174076, 525298, 1582036, 4758394, 14299756, 42948418, 128943556, 387027274, 1161475036, 3485211538, 10457207476, 31374768154, 94130595916, 282404370658, 847238277796, 2541765165034, 7625396158396 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,2
COMMENTS
The number of ways of partitioning the multiset {1, 1, 2, 3, ..., n-1} into exactly two, four and five nonempty parts are given in A083329, A168584 and A168585, respectively.
LINKS
FORMULA
For a>=3, a(n) = 3^(n-2) - 3*2^(n-3) + 1.
E.g.f.: 3*e^(3x) - 3*e^(2x) + e^x (shifted).
O.g.f.: x^3*(1-2x+3x^2)/((1-x)*(1-2x)*(1-3x)).
a(n) = A126644(n-3). - R. J. Mathar, Dec 11 2009
EXAMPLE
The partitions of {1,1,2,3} into exactly three nonempty parts are {{1},{1},{2,3}}, {{1},{2},{1,3}}, {{1},{3},{1,2}} and {{2},{3},{1,1}}.
MAPLE
A168583:=n->3^(n-2)-3*2^(n-3)+1: seq(A168583(n), n=3..40); # Wesley Ivan Hurt, Dec 12 2015
MATHEMATICA
f1[n_] := 3^(n - 2) - 3 2^(n - 3) + 1; Table[f1[n], {n, 3, 25}]
PROG
(Magma) [3^(n-2) - 3*2^(n-3) + 1: n in [3..35]]; // Vincenzo Librandi, Dec 12 2015
CROSSREFS
Sequence in context: A034514 A263851 A126644 * A092688 A267466 A255299
KEYWORD
nonn,easy
AUTHOR
Martin Griffiths, Nov 30 2009
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)