A119874 Sizes of successive clusters in f.c.c. lattice centered at an octahedral hole.

6, 14, 38, 38, 68, 92, 116, 116, 164, 188, 236, 236, 266, 298, 370, 370, 418, 466, 490, 490, 586, 610, 682, 682, 736, 784, 856, 856, 904, 976, 1048, 1048, 1144, 1168, 1264, 1264, 1312, 1368, 1464, 1464, 1566, 1638, 1686, 1686, 1830, 1878, 1926, 1926, 1974

Offset

0,1

References

N. J. A. Sloane and B. K. Teo, Theta series and magic numbers for close-packed spherical clusters, J. Chem. Phys. 83 (1985) 6520-6534.

Links

N. J. A. Sloane, Table of n, a(n) for n = 0..9999

Wouter Meeussen, ConvexHull3D package & demo-file.

Formula

Partial sums of A005887, which has an explicit generating function.

Maple

maxd:=20001: read format: temp0:=trunc(evalf(sqrt(maxd)))+2: a:=0: for i from -temp0 to temp0 do a:=a+q^( (i+1/2)^2): od: th2:=series(a, q, maxd): a:=0: for i from -temp0 to temp0 do a:=a+q^(i^2): od: th3:=series(a, q, maxd): th4:=series(subs(q=-q, th3), q, maxd):
t1:=series((th3^3-th4^3)/(2*q), q, maxd): t1:=series(subs(q=sqrt(q), t1), q, floor(maxd/2)): t2:=seriestolist(t1): t4:=0; for n from 1 to nops(t2) do t4:=t4+t2[n]; lprint(n-1, t4); od: # N. J. A. Sloane, Aug 09 2006

Crossrefs

Cf. A005887.

Cf. A119869, Properties of Waterman polyhedra of void center type: A119875 [vertices], A119876 [faces], A119877 [edges], A119878 [volume].

Sequence in context: A036387 A053560 A229441 * A344380 A270127 A269511

Adjacent sequences: A119871 A119872 A119873 * A119875 A119876 A119877

Keyword

nonn

Author

Hugo Pfoertner, Jun 05 2006

Extensions

Edited by N. J. A. Sloane, Aug 09 2006

Status

approved