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Search: id:A114438
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| A114438 |
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Number of Barlow packings that repeat after n (or a divisor of n) layers. |
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+0
4
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| 0, 1, 1, 2, 1, 4, 3, 8, 8, 18, 21, 48, 63, 133, 205, 412, 685, 1354, 2385, 4644, 8496, 16431, 30735, 59344, 112531, 217246, 415628, 803210, 1545463, 2991192, 5778267, 11201884, 21702708, 42141576, 81830748, 159140896, 309590883, 602938099, 1174779397, 2290920128
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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See A011768 for the number of Barlow packings that repeat after exactly n layers.
Like A056353 but with additional restriction that adjacent beads must have different colors.
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REFERENCES
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E. Estevez-Rams, C. Azanza-Ricardo, J. Martinez-Garcia and B. Argon-Frenadez, On the algebra of binary codes representing closed-packed staking sequences, Acta Cryst. A61 (2006), 201-208.
T. J. McLarnan, The numbers of polytypes ..., Zeits. Krist. 155, 269-291 (1981). [See P'(N) on page 272.]
J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discr. Comp. Geom., 13 (1995), 383-403.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..500
R. M. Thompson and R. T. Downs, Systematic generation of all nonequivalent close-packed stacking sequences..., Acta Cryst. B57 (2001), 766-771; B58 (2002), 153.
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MAPLE
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with(numtheory); read transforms; M:=500;
A:=proc(N, d) if d mod 3 = 0 then 2^(N/d) else (1/3)*(2^(N/d)+2*cos(Pi*N/d)); fi; end;
E:=proc(N) if N mod 2 = 0 then N*2^(N/2) + add( did(N/2, d)*phi(2*d)*2^(N/(2*d)), d=1..N/2) else (N/3)*(2^((N+1)/2)+2*cos(Pi*(N+1)/2)); fi; end;
PP:=proc(N) (1/(4*N))*(add(did(N, d)*phi(d)*A(N, d), d=1..N)+E(N)); end; for N from 1 to M do lprint(N, PP(N)); od: (N. J. A. Sloane, Aug 10 2006)
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CROSSREFS
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Cf. A027671, A056353.
Sequence in context: A005291 A106624 A028297 this_sequence A109195 A032662 A138509
Adjacent sequences: A114435 A114436 A114437 this_sequence A114439 A114440 A114441
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Feb 28 2006; more terms, Aug 10 2006
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