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!)
A088536 Number of unimodal functions [1..n]->[1..n]. 6
1, 4, 22, 130, 791, 4900, 30738, 194634, 1241383, 7963384, 51325352, 332095816, 2155894508, 14035149748, 91593941402, 599021799242, 3924954250975, 25760310654100, 169322682857430, 1114452091832130, 7344021912458295, 48448974411575280, 319942093205166840, 2114743632331515480 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{k=0..n-1} binomial(2k+n-1,2k).
Recurrence: 36*n*(2*n-3)*a(n) = 2*(269*n^2-549*n+235)*a(n-1) - (359*n^2-1062*n+907)*a(n-2) + 6*(3*n-8)*(3*n-7)*a(n-3). - Vaclav Kotesovec, Oct 14 2012
a(n) ~ 27^n/(5*2^(2*n-1)*sqrt(3*Pi*n)). - Vaclav Kotesovec, Oct 14 2012
It appears that a(n) = Sum_{k = 0..2*n-2} (-1)^k*binomial(n+k,k). - Peter Bala, Oct 08 2021
EXAMPLE
From Joerg Arndt, May 10 2013: (Start)
The a(3) = 22 unimodal maps [1,2,3]->[1,2,3] are
01: [ 1 1 1 ]
02: [ 1 1 2 ]
03: [ 1 1 3 ]
04: [ 1 2 1 ]
05: [ 1 2 2 ]
06: [ 1 2 3 ]
07: [ 1 3 1 ]
08: [ 1 3 2 ]
09: [ 1 3 3 ]
10: [ 2 1 1 ]
11: [ 2 2 1 ]
12: [ 2 2 2 ]
13: [ 2 2 3 ]
14: [ 2 3 1 ]
15: [ 2 3 2 ]
16: [ 2 3 3 ]
17: [ 3 1 1 ]
18: [ 3 2 1 ]
19: [ 3 2 2 ]
20: [ 3 3 1 ]
21: [ 3 3 2 ]
22: [ 3 3 3 ]
(End)
MATHEMATICA
Table[Sum[Binomial[2k+n-1, 2k], {k, 0, n-1}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 14 2012 *)
PROG
(PARI) a(n) = sum(k=0, n-1, binomial(2*k+n-1, 2*k)); \\ Joerg Arndt, May 10 2013
CROSSREFS
Main diagonal of A071920.
Cf. A225006 (unimodal maps [1..n]->[1..n+1]).
Sequence in context: A086682 A261399 A155862 * A066380 A180899 A007195
KEYWORD
nonn
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 16 2003
EXTENSIONS
More terms from David Wasserman, Aug 09 2005
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 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)