|
| |
| |
|
|
|
0, 4, 12, 28, 60, 124, 252, 508, 1020, 2044, 4092, 8188, 16380, 32764, 65532, 131068, 262140, 524284, 1048572, 2097148, 4194300, 8388604, 16777212, 33554428, 67108860, 134217724, 268435452, 536870908, 1073741820, 2147483644
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 2,2
|
|
|
COMMENTS
| Number of permutations of [n] with 2 sequences.
Number of 2 X n binary matrices that avoid simultaneously the right angled numbered polyomino patterns (ranpp) (00;1) and (11;0). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1<i2, j1<j2 and these elements are in same relative order as those in the triple (x,y,z). - Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 11 2004
The number of edges in the dual Edwards-Venn digram graph with n-1 digits when n>2.
Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 28 2010: (Start)
a(n) = A175164(2*n)/A140504(n+2);
a(2*n) = A052548(n)*A000918(n) for n>0;
a(n) = A173787(n,2). (End)
|
|
|
REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 261.
I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.
A. W. F. Edwards, Cogwheels of the Mind, Johns Hopkins University Press, 2004, p. 82.
|
|
|
LINKS
| S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, University of Kentucky Research Reports (2004).
|
|
|
FORMULA
| O.g.f.: 4x^3/((1-x)(1-2x)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 07 2008]
a(n) = a(n-1)+2^(n-1) (with a(2)=0). [From Vincenzo Librandi, Nov 22 2010]
|
|
|
MAPLE
| [seq (stirling2(n, 2)*4, n=1..30)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 06 2006
|
|
|
MATHEMATICA
| a=0; lst={}; k=4; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 15 2008]
|
|
|
PROG
| (PARI) a(n)=if(n<2, 0, 2^n-4)
(Other) sage: [gaussian_binomial(n, 1, 2)-3 for n in xrange(2, 32)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 31 2009]
|
|
|
CROSSREFS
| Sequence in context: A186924 A179023 * A173033 A034508 A173380 A002932
Adjacent sequences: A028396 A028397 A028398 * A028400 A028401 A028402
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Additional comments from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 2/12/01
|
| |
|
|
