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A099003
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Number of 4 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (10;0) and (11;0).
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8
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1, 16, 46, 106, 226, 466, 946, 1906, 3826, 7666, 15346, 30706, 61426, 122866, 245746, 491506, 983026, 1966066, 3932146, 7864306, 15728626, 31457266, 62914546, 125829106, 251658226, 503316466, 1006632946, 2013265906, 4026531826
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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+n) - 2^m - 2^n + 2.
Binomial transform of 1,15,15,... (15 infinitely repeated). - Gary W. Adamson, Apr 29 2008
The binomial transform of [1, c, c, c, ...] has the terms a(n) = 1 - c + c*2^(n-1) if the offset 1 is chosen. The o.g.f. of the a(n) is x*(1+(c-2)x)/((2x-1)*(x-1)). This applies to A139634 with c=10, to A139635 with c=11, to A139697 with c=12, to A139698 with c=25 and to A099003, A139700, A139701 accordingly. - R. J. Mathar, May 11 2008
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LINKS
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FORMULA
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a(n) = 15*2^n - 14.
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MATHEMATICA
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LinearRecurrence[{3, -2}, {1, 16}, 40] (* Harvey P. Dale, May 20 2018 *)
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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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STATUS
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approved
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