|
| |
| |
|
|
|
4, 10, 16, 22, 28, 34, 40, 46, 52, 58, 64, 70, 76, 82, 88, 94, 100, 106, 112, 118, 124, 130, 136, 142, 148, 154, 160, 166, 172, 178, 184, 190, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268, 274, 280, 286, 292, 298, 304, 310, 316, 322, 328
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| Number of 2 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01,1) 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 the same relative order as those in the triple (x,y,z). In general, the number of m X n 0-1 matrices in question is given by (n+2)*2^(m-1)+2*m*(n-1)-2 for m>1 and n>1. [Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 12 2004]
If Y is a 4-subset of an n-set X then, for n>=4, a(n-4) is the number of 3-subsets of X having at least two elements in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 08 2007
A008615(a(n)) = n+1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 27 2008
4th transversal numbers (or 4-transversal numbers): Numbers of the 4th column of positive numbers in the square array of nonnegative and polygonal numbers A139600. Also, numbers of the 4th column in the square array A057145. - Omar E. Pol (info(AT)polprimos.com), May 02 2008
A157176(a(n)) = A067412(n+1). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 24 2009]
a(n) is the maximum number such that there exists an edge coloring of the complete graph with a(n) vertices using n colors and every subgraph whose edges are of the same color (subgraph induced by edge color) is planar. [Srikanth K S, sriperso@gmail.com, Dec 18 2010]
|
|
|
LINKS
| Tanya Khovanova, Recursive Sequences
S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
|
|
|
FORMULA
| a(n) = A016789(n)*2. - Omar E. Pol (info(AT)polprimos.com), May 02 2008
a(n) = sqrt(A016958(n)). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2009
a(n) = 2*(6*n+1)-a(n-1) (with a(0)=4). - Vincenzo Librandi, Nov 20 2010
a(n) = floor((sqrt(36*n^2-36*n+1)+6*n+1)/2). - Srikanth K S, Dec 18 2010
G.f.: 2*(2+x)/(1-2*x+x^2). a(n) = 2*a(n-1)-a(n-2). - Colin Barker, Jan 30 2012
|
|
|
MATHEMATICA
| Range[4, 1000, 6] (* From Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), May 27 2011 *)
|
|
|
CROSSREFS
| Cf. A008588, A016921, A016933, A016945, A016969.
Cf. A000217, A017329, A057145, A139600, A139606.
A016958 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2009]
Sequence in context: A140493 A141427 A189932 * A109273 A161644 A184527
Adjacent sequences: A016954 A016955 A016956 * A016958 A016959 A016960
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
