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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 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A004015, A004215, A055039. 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 Adjacent sequences:  A119866 A119867 A119868 * A119870 A119871 A119872 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

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Last modified January 27 15:14 EST 2020. Contains 331295 sequences. (Running on oeis4.)