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A010369 Number of points of L1 norm 2n in root system version of E_8 lattice. 2
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; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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 Nov 27 1998.

REFERENCES

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.

LINKS

Table of n, a(n) for n=0..24.

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

FORMULA

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.

MAPLE

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.

CROSSREFS

Cf. A010368.

Sequence in context: A135983 A101327 A035880 * A121374 A252487 A160638

Adjacent sequences:  A010366 A010367 A010368 * A010370 A010371 A010372

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Simon Plouffe

STATUS

approved

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Last modified June 28 04:43 EDT 2017. Contains 288813 sequences.