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A011768 Number of Barlow packings that repeat after exactly n layers. 2
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; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..200

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 (2005), 201-208.

T. J. McLarnan, The numbers of polytypes in close-packings and related structures, Zeits. Krist. 155, 269-291 (1981).

MAPLE

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

CROSSREFS

Cf. A114438.

Sequence in context: A034901 A275390 A109976 * A052487 A067951 A131862

Adjacent sequences:  A011765 A011766 A011767 * A011769 A011770 A011771

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Michael OKeeffe (MOKeeffe(AT)asu.edu)

EXTENSIONS

More terms from N. J. A. Sloane, Aug 10 2006

STATUS

approved

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Last modified January 21 11:21 EST 2019. Contains 319354 sequences. (Running on oeis4.)