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Search: id:A100314
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| A100314 |
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Number of 2 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1). 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 2^m+2^n+2(nm-n-m). |
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+0
3
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| 4, 8, 14, 24, 42, 76, 142, 272, 530, 1044, 2070, 4120, 8218, 16412, 32798, 65568, 131106, 262180, 524326, 1048616, 2097194, 4194348, 8388654, 16777264, 33554482, 67108916, 134217782, 268435512, 536870970, 1073741884
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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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) = 2^n + 2*n
O.g.f.: 2x(2-4x+x^2)/((1-x)^2*(1-2x)). a(n+1)-a(n) = A052548(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 13 2008
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MATHEMATICA
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lst={}; s=-1; Do[s+=s+n; AppendTo[lst, Abs[s]], {n, -2, 5!, 2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 18 2008]
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CROSSREFS
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Cf. m=3: A100315; m=4: A100316.
Sequence in context: A060064 A045474 A131831 this_sequence A105143 A020185 A008029
Adjacent sequences: A100311 A100312 A100313 this_sequence A100315 A100316 A100317
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KEYWORD
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nonn
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AUTHOR
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Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 13 2004
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