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 A056326 Number of reversible string structures with n beads using exactly two different colors. 9
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A string and its reverse are considered to be equivalent. Permuting the colors will not change the structure. REFERENCES 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] LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3, 0, -6, 4). FORMULA a(n) = A005418(n) - 1. From Colin Barker, Nov 25 2012: (Start) 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) MATHEMATICA 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 *) CROSSREFS Column k=2 of A284949 and of A291883. Cf. A056309. Sequence in context: A048082 A089089 A014495 * A280247 A261049 A122893 Adjacent sequences:  A056323 A056324 A056325 * A056327 A056328 A056329 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified February 20 19:41 EST 2020. Contains 332084 sequences. (Running on oeis4.)