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Search: id:A011768
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| A011768 |
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Number of Barlow packings that repeat after exactly n layers. |
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+0
2
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| 0, 1, 1, 1, 1, 2, 3, 6, 7, 16, 21, 43, 63, 129, 203, 404, 685, 1343, 2385, 4625, 8492, 16409, 30735, 59290, 112530, 217182, 415620, 803076, 1545463, 2990968, 5778267, 11201472, 21702686, 42140890, 81830744, 159139498, 309590883, 602935713, 1174779333, 2290915478
(list; graph; listen)
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OFFSET
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1,6
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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).
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..200
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MAPLE
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with(numtheory); read transforms; M:=200;
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 t1[N]:=PP(N); od:
P:=proc(N) local s, d; s:=0; for d from 1 to N do if N mod d = 0 then s:=s+mobius(N/d)*t1[d]; fi; od: s; end; for N from 1 to M do lprint(N, P(N)); od: (N. J. A. Sloane, Aug 10 2006)
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CROSSREFS
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Cf. A114438.
Sequence in context: A137604 A034901 A109976 this_sequence A052487 A067951 A131862
Adjacent sequences: A011765 A011766 A011767 this_sequence A011769 A011770 A011771
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), MOKeeffe(AT)asu.edu (Michael OKeeffe)
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EXTENSIONS
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More terms from N. J. A. Sloane (njas(AT)research.att.com), Aug 10 2006
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