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A095977
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Expansion of 2*x / ((1+x)^2*(1-2*x)^2).
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2
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2, 4, 14, 32, 82, 188, 438, 984, 2202, 4852, 10622, 23056, 49762, 106796, 228166, 485448, 1029162, 2174820, 4582670, 9631360, 20194802, 42253724, 88235734, 183927992, 382769082, 795364308, 1650380958, 3420066544, 7078742402
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OFFSET
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1,1
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COMMENTS
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Number of 2 X 2 tiles in all tilings of a 3 X (n+1) rectangle with 1 X 1 and 2 X 2 square tiles. - Emeric Deutsch, Feb 18 2007
The terms of this sequence have a primitive divisor for all terms beyond the 4th if and only if n is not of the form 4k+2, for some nonnegative integer k. - Anthony Flatters (Anthony.Flatters(AT)uea.ac.uk), Aug 17 2007
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LINKS
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FORMULA
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a(n) = (1/27)*((3*n + 2)*2^(n + 2) - (6*n + 8)*(-1)^n).
a(n) = Sum_{k=0..floor((n+1)/2)} k*2^k*binomial(n+1-k,k). - Emeric Deutsch, Feb 18 2007
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MAPLE
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a:=n->n/9*2^(n+2)+1/27*2^(n+3)-2*n/9*(-1)^n-8/27*(-1)^n: seq(a(n), n=1..30); # Emeric Deutsch, Feb 18 2007
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MATHEMATICA
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Table[(1/27)*((3*n + 2)*2^(n + 2) - (6*n + 8)*(-1)^n) , {n, 1, 50}] (* G. C. Greubel, Dec 28 2016 *)
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PROG
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(PARI) Vec(2*x / ((1+x)^2 * (1-2*x)^2) + O(x^50)) \\ Michel Marcus, Nov 07 2015
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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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