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A100312
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Number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (10;0) and (01;1).
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4
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1, 8, 32, 104, 304, 832, 2176, 5504, 13568, 32768, 77824, 182272, 421888, 966656, 2195456, 4947968, 11075584, 24641536, 54525952, 120061952, 263192576, 574619648, 1249902592, 2709520384, 5855248384, 12616466432, 27111981056, 58116276224, 124285616128
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OFFSET
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0,2
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COMMENTS
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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 the g.f. 2*x*y/(1-2*(x+y-x*y)).
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LINKS
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FORMULA
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G.f.: 1 + 8*x*(1-x)^2/(1-2*x)^3.
a(n) = 2^(n-1) * (n^2 + 5*n + 2).
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MATHEMATICA
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Table[2^(n-1)*(n^2+5*n+2), {n, 0, 50}] (* G. C. Greubel, Feb 01 2023 *)
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PROG
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(PARI) vector(50, n, (n^2 + 5*n + 2) * 2^(n-1)) \\ Michel Marcus, Dec 01 2014
(Magma) [2^(n-1)*(n^2+5*n+2): n in [0..50]]; // G. C. Greubel, Feb 01 2023
(SageMath) [2^(n-1)*(n^2+5*n+2) for n in range(51)] # G. C. Greubel, Feb 01 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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