login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080337 Bisection of A080107. 4
1, 3, 12, 59, 339, 2210, 16033, 127643, 1103372, 10269643, 102225363, 1082190554, 12126858113, 143268057587, 1778283994284, 23120054355195, 314017850216371, 4444972514600178, 65435496909148513, 999907522895563403 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Number of symmetric positions of non-attacking rooks on upper-diagonal part of 2n X 2n chessboard.

Number of length-n restricted growth strings (RGS) [s(0),s(1),...,s(n-1)] where s(0)=0 and s(k)<=2+max(prefix) for k>=1, see example. [Joerg Arndt, Apr 25 2010]

LINKS

Table of n, a(n) for n=1..20.

Joerg Arndt, Matters Computational (The Fxtbook), section 17.3.4, pp. 364-366

J. Quaintance, Letter representations of rectangular m x n x p proper arrays

FORMULA

Binomial transform of A002872 (sorting numbers).

E.g.f.: exp(x+exp(x)+exp(2*x)/2-3/2) = exp(x+sum(j=1,2, (exp(j*x)-1)/j ) ). [Joerg Arndt, Apr 29 2011]

EXAMPLE

From Joerg Arndt, Apr 25 2010: (Start)

For n=0 there is one empty string (term a(0)=0 not included here); for n=1 there is one string [0]; for n=2 there are 3 strings [00], [01], and [02];

for n=3 there are a(3)=12 strings (in lexicographic order):

01: [000],

02: [001],

03: [002],

04: [010],

05: [011],

06: [012],

07: [013],

08: [020],

09: [021],

10: [022],

11: [023],

12: [024].

(End)

MATHEMATICA

Table[Sum[ Binomial[n, k] A002872[[k + 1]], {k, 0, n}], {n, 0, 24}]

PROG

(PARI) x='x+O('x^66);

egf=exp(x+exp(x)+exp(2*x)/2-3/2); /* = 1 +3*x +6*x^2 +59/6*x^3 +113/8*x^4 +... */

Vec(serlaplace(egf)) /* Joerg Arndt, Apr 29 2011 */

CROSSREFS

Cf. A002872, A080107.

Sequence in context: A192768 A179325 A064856 * A196710 A196711 A101054

Adjacent sequences:  A080334 A080335 A080336 * A080338 A080339 A080340

KEYWORD

nonn

AUTHOR

Wouter Meeussen, Mar 18 2003

EXTENSIONS

Comment corrected by Wouter Meeussen, Aug 14 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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 22 21:40 EDT 2017. Contains 286906 sequences.