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Search: id:A016957
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| 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
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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]
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LINKS
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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.
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FORMULA
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a(n) = A016789(n)*2. - Omar E. Pol (info(AT)polprimos.com), May 02 2008
a(n) = (A000217(4)-4)*n+4 = (10-4)n+4 = 6n+4 = 2(3n+2). - Omar E. Pol (info(AT)polprimos.com), May 02 2008
a(n) = sqrt(A016958 a(n)). [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2009]
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MAPLE
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a[1]:=-2:for n from 2 to 100 do a[n]:=a[n-1]+6 od: seq(a[n], n=2..47); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
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MATHEMATICA
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f[n_]:=6*n+4; lst={}; Do[a=f[n]; AppendTo[lst, a], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 25 2009]
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PROGRAM
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(Other) sage: [i+4 for i in range(275) if gcd(i, 6) == 6] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 20 2009]
(Other) sage: [crt(4, n, 3, 5) for n in xrange(4, 50)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 30 2009]
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CROSSREFS
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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: A043385 A140493 A141427 this_sequence A109273 A161644 A049881
Adjacent sequences: A016954 A016955 A016956 this_sequence A016958 A016959 A016960
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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