A056326 Number of reversible string structures with n beads using exactly two different colors.

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

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: A089089 A369854 A014495 * A280247 A261049 A122893

Adjacent sequences: A056323 A056324 A056325 * A056327 A056328 A056329

Keyword

nonn,easy

Author

Marks R. Nester

Status

approved