A010369 Number of points of L1 norm 2n in root system version of E_8 lattice.

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

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.

Links

Ray Chandler, 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 (pdf).

Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

P. Solé, Counting lattice points in pyramids, Discr. Math. 139 (1995), 381-392.

Index entries for linear recurrences with constant coefficients, signature (0, 8, 0, -28, 0, 56, 0, -70, 0, 56, 0, -28, 0, 8, 0, -1).

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: A101327 A368676 A035880 * A351247 A303324 A121374

Adjacent sequences: A010366 A010367 A010368 * A010370 A010371 A010372

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Status

approved