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A239917 Theta series of 16-dimensional lattice OBW16, an overlattice of the Barnes-Wall lattice BW16. 0
1, 0, 0, 512, 4320, 18432, 61440, 193536, 522720, 1126400, 2211840, 4584960, 8960640, 14764032, 23224320, 40221696, 67154400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The 512 vectors of norm 3 form a spherical 5-design (see Neumaier, 1981). The corresponding configuration of 256 lines in 16-space was studied by Shult and Yanushka, 1980.

LINKS

Table of n, a(n) for n=0..16.

G. Nebe and N. J. A. Sloane, Home page for this lattice

A. Neumaier, Combinatorial configurations in terms of distances, Report 81-09-Wiskunde, Tech. Univ. Eindhoven, 1981.

A. Neumaier, Lattices of simplex type, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 145--160. MR0699768 (85f:05040). See Example 3.

Ernest Shult, Arthur Yanushka, Arthur, Near n-gons and line systems, Geom. Dedicata 9 (1980), no. 1, 1--72. MR0566437 (82b:51018).

EXAMPLE

The theta series is 1 + 512*q^3 + 4320*q^4 + 18432*q^5 + 61440*q^6 + 193536*q^7 + 522720*q^8 + 1126400*q^9 + 2211840*q^10 + 4584960*q^11 + 8960640*q^12 + 14764032*q^13 + 23224320*q^14 + 40221696*q^15 + 67154400*q^16 + O(q^17).

PROG

(MAGMA)

L:=LatticeWithGram(16, [3,

-1, 3,

-1, -1, 3,

1, -1, 1, 3,

0, 1, 0, -1, 3,

-1, 0, 0, -1, -1, 3,

1, 0, 0, 1, -1, -1, 3,

-1, 0, 1, 0, 1, -1, -1, 3,

1, 0, -1, 0, -1, 1, 1, -1, 3,

-1, 0, 1, 0, -1, 0, 0, 1, -1, 3,

0, 1, 0, 1, 0, 0, 1, -1, 0, 0, 3,

1, -1, 1, 1, -1, 0, 1, -1, 0, 0, 0, 3,

-1, 0, 1, 1, 0, -1, 0, 1, -1, 1, 0, 0, 3,

0, 0, 1, 0, 1, 0, -1, 1, -1, 0, 0, 0, -1, 3,

1, 1, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, -1, 1, 3,

1, -1, -1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 3]);

T<q>:=ThetaSeries(L, 16);

T;

CROSSREFS

Sequence in context: A186798 A017067 A186845 * A114287 A061209 A017259

Adjacent sequences:  A239914 A239915 A239916 * A239918 A239919 A239920

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Apr 13 2014

STATUS

approved

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Last modified July 11 22:52 EDT 2020. Contains 335652 sequences. (Running on oeis4.)