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
Keywords
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
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
Comments