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A008401
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Coordination sequence for {E_6}* lattice.
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2
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1, 54, 828, 5202, 20376, 60030, 146484, 312858, 605232, 1084806, 1830060, 2938914, 4530888, 6749262, 9763236, 13770090, 18997344, 25704918, 34187292, 44775666, 57840120, 73791774, 93084948
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OFFSET
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0,2
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REFERENCES
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M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
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LINKS
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J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
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FORMULA
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a(n) = 6*n*(3*n^4 + 5*n^2 + 1), n > 0.
G.f.: (1+48*x+519*x^2+1024*x^3+519*x^4+48*x^5+x^6)/(1-x)^6.
E.g.f.: 1 + 6*exp(x)*x*(9 + 60*x + 80*x^2 + 30*x^3 + 3*x^4). - Stefano Spezia, Apr 15 2022
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MATHEMATICA
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Join[{1}, Table[18 n^5+30 n^3+6 n, {n, 30}]] (* Harvey P. Dale, May 16 2012 *)
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PROG
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(Magma) [1] cat [6*n*(3*n^4+5*n^2+1): n in [1..40]]; // G. C. Greubel, May 30 2023
(SageMath) [6*n*(3*n^4+5*n^2+1) +int(n==0) for n in range(41)] # G. C. Greubel, May 30 2023
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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