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A119869
Sizes of successive clusters in f.c.c. lattice centered at a lattice point.
8
1, 13, 19, 43, 55, 79, 87, 135, 141, 177, 201, 225, 249, 321, 321, 369, 381, 429, 459, 531, 555, 603, 627, 675, 683, 767, 791, 887, 935, 959, 959, 1055, 1061, 1157, 1205, 1253, 1289, 1409, 1433, 1481, 1505, 1553, 1601, 1721, 1745, 1865, 1865, 1961, 1985, 2093, 2123
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
Paul Bourke, Waterman Polyhedra.
Paul Bourke, On-line generator
Martin Kraus, Live Graphics3d
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
Cf. A055039 [missing polyhedra]. Properties of Waterman polyhedra: A119870 [vertices], A119871 [faces], A119872 [edges], A119873 [volume]. Waterman polyhedra with different centers: A119874, A119875, A119876, A119877, A119878.
Sequence in context: A216101 A096455 A124199 * A272200 A106904 A106903
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