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

Author

Hugo Pfoertner, Jun 05 2006

Keywords

• nonn

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.

Crossrefs

Cf. A005887.

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

Programs

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

Formula

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

Extensions

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