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Search: id:A010369
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| A010369 |
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Number of points of L1 norm 2n in root system version of E_8 lattice. |
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+0
3
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| 1, 0, 128, 0, 2944, 1024, 31616, 15360, 199424, 101376, 877696, 439296, 3011200, 1464320, 8630144, 4073472, 21607936, 9922560, 48713856, 21829632, 101009792, 44301312, 195640192, 84198400, 358064384
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also, coordination sequence for diamond structure D^+_8. (Edges defined by l_1 norm = 1.) - J. Serra-Sagrista (jserra(AT)ccd.uab.es). Confirmed by N. J. A. Sloane (njas(AT)research.att.com) Nov 27 1998.
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REFERENCES
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J. Serra-Sagrista, Enumeration of lattice points in l_1 norm, Information Processing Letters, 76, no. 1-2 (2000), 39-44.
P. Sole', Counting lattice points in pyramids, Discr. Math. 139 (1995), 381-392.
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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 (Abstract, pdf, ps).
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FORMULA
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G.f.: (1/2)*((1+z^2)^8+256*z^8)/(1-z^2)^8 + (1/2)*(1-z^2)^8/(1+z^2)^8.
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MAPLE
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1/2*((1+z^2)^8+256*z^8)/(1-z^2)^8+1/2*(1-z^2)^8/(1+z^2)^8
f := proc(m) local k, t1; t1 := 2^(n-1)*binomial((n+2*m)/2-1, n-1); if m mod 2 = 0 then t1 := t1+add(2^k*binomial(n, k)*binomial(m-1, k-1), k=0..n); fi; t1; end; where n=8.
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CROSSREFS
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Cf. A010368.
Sequence in context: A135983 A101327 A035880 this_sequence A121374 A160638 A097758
Adjacent sequences: A010366 A010367 A010368 this_sequence A010370 A010371 A010372
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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