OFFSET
0,2
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
Paul Bourke, Waterman Polyhedra.
Paul Bourke, On-line generator
Martin Kraus, Live Graphics3d
Mirek Majewski, Dedicated commands in MuPAD
Wouter Meeussen, ConvexHull3D package & demo-file.
Mark Newbold, Waterman Polyhedra. CCPOLY Java Applet.
Steve Waterman, Waterman Polyhedron.
Steve Waterman, Missing numbers formula
FORMULA
Partial sums of A004015, 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, 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
MATHEMATICA
a[n_] := Sum[SquaresR[3, 2k], {k, 0, n}]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jul 12 2012, after formula *)
Accumulate[SquaresR[3, 2*Range[0, 70]]] (* Harvey P. Dale, Jun 01 2015 *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Hugo Pfoertner, May 26 2006
EXTENSIONS
Edited by N. J. A. Sloane, Aug 09 2006
Additional links from Steve Waterman, Nov 26 2006
STATUS
approved