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A056326
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Number of reversible string structures with n beads using exactly two different colors.
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9
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0, 1, 2, 5, 9, 19, 35, 71, 135, 271, 527, 1055, 2079, 4159, 8255, 16511, 32895, 65791, 131327, 262655, 524799, 1049599, 2098175, 4196351, 8390655, 16781311, 33558527, 67117055, 134225919, 268451839, 536887295, 1073774591, 2147516415, 4295032831, 8590000127
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OFFSET
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1,3
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COMMENTS
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A string and its reverse are considered to be equivalent. Permuting the colors will not change the structure.
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REFERENCES
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M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
G.f.: x^2*(x^2+x-1)/((x-1)*(2*x-1)*(2*x^2-1)). (End)
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MATHEMATICA
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Table[(StirlingS2[n, 2] + StirlingS2[Floor[n/2]+1, 2])/2, {n, 1, 30}] (* Robert A. Russell, Jan 29 2018 *)
LinearRecurrence[{3, 0, -6, 4}, {0, 1, 2, 5}, 35] (* or *)
Rest@ CoefficientList[Series[x^2*(x^2 + x - 1)/((x - 1) (2 x - 1) (2 x^2 - 1)), {x, 0, 35}], x] (* Michael De Vlieger, Jan 31 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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