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A100315
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Number of 3 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1).
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4
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1, 8, 14, 22, 34, 54, 90, 158, 290, 550, 1066, 2094, 4146, 8246, 16442, 32830, 65602, 131142, 262218, 524366, 1048658, 2097238, 4194394, 8388702, 16777314, 33554534, 67108970, 134217838, 268435570, 536871030, 1073741946, 2147483774, 4294967426, 8589934726
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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 2^m + 2^n + 2*(n*m-n-m).
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LINKS
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FORMULA
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a(n) = 2^n + 4*n + 2 for n>0, a(0)=1.
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n > 3.
G.f.: 1 + 2*x*(4 - 9*x + 3*x^2)/((1-x)^2*(1-2*x)). (End)
E.g.f.: exp(2*x) + 2*(1+2*x)*exp(x) - 2. - G. C. Greubel, Feb 01 2023
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MATHEMATICA
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PROG
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(Magma) [2^n+4*n+2*(1-0^n): n in [0..40]]; // G. C. Greubel, Feb 01 2023
(SageMath) [2^n+4*n+2*(1-0^n) for n in range(41)] # 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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