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A056357
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Number of bracelet structures using exactly two different colored beads.
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1
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0, 1, 1, 3, 3, 7, 8, 17, 22, 43, 62, 121, 189, 361, 611, 1161, 2055, 3913, 7154, 13647, 25481, 48733, 92204, 176905, 337593, 649531, 1246862, 2405235, 4636389, 8964799, 17334800
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Turning over will not create a new bracelet. Permuting the colors of the beads will not change the structure.
Also the number of distinct twills of period n. [Gruenbaum and Shephard]
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REFERENCES
| B. Gruenbaum and G. C. Shephard, Satins and twills: an introduction to the geometry of fabrics, Math. Mag., 53 (1980), 139-161. See Theorem 2. [From N. J. A. Sloane, Jul 13 2011]
M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia.
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FORMULA
| A000011(n)-1.
For an explicit formula see the Maple program.
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MAPLE
| with(numtheory);
rho:=n->(3+(-1)^n)/2;
f:=n->2^((n+rho(n))/2-2) + (1/(4*n))*(add(phi(d)*rho(d)*2^(n/d), d in divisors(n))) - 1;
(from N. J. A. Sloane, Jul 13 2011)
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CROSSREFS
| Cf. A056295.
Sequence in context: A110618 A108046 A116157 * A144554 A177936 A143088
Adjacent sequences: A056354 A056355 A056356 * A056358 A056359 A056360
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KEYWORD
| nonn
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AUTHOR
| Marks R. Nester (nesterm(AT)dpi.qld.gov.au)
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