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A008412
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Coordination sequence for 4-dimensional cubic lattice (points on surface of 4-dimensional cross-polytope).
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12
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1, 8, 32, 88, 192, 360, 608, 952, 1408, 1992, 2720, 3608, 4672, 5928, 7392, 9080, 11008, 13192, 15648, 18392, 21440, 24808, 28512, 32568, 36992, 41800, 47008, 52632, 58688, 65192, 72160, 79608
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OFFSET
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0,2
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COMMENTS
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Coordination sequence for 4-dimensional cyclotomic lattice Z[zeta_8].
If Y_i (i=1,2,3,4) are 2-blocks of a (n+4)-set X then a(n-3) is the number of 7-subsets of X intersecting each Y_i (i=1,2,3,4). - Milan Janjic, Oct 28 2007
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REFERENCES
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M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv math.CO/0508136.
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (Abstract, pdf, ps).
Milan Janjic, Two Enumerative Functions
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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G.f.: ((1+x)/(1-x))^4.
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MAPLE
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8/3*n^3+16/3*n;
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MATHEMATICA
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CoefficientList[Series[((1+x)/(1-x))^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 8, 32, 88, 192}, 41] (* From Harvey P. Dale, June 10 2011 *)
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PROG
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(PARI) a(n)=if(n, 8*(n^2+2)*n/3, 1) \\ Charles R Greathouse IV, Jun 10 2011
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CROSSREFS
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Cf. A001845.
First differences of A001846.
Sequence in context: A211633 A130809 A018839 * A014819 A033155 A132117
Adjacent sequences: A008409 A008410 A008411 * A008413 A008414 A008415
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KEYWORD
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nonn,easy,nice,changed
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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