A063863 - OEIS

A063863

Theta series of A15 packing with respect to origin.

1, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 8, 12, 0, 0, 6, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 12, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 24, 36, 0, 0, 8, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 6, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 24, 48, 0, 0, 24, 0, 0, 0, 0, 24, 0

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OFFSET

0,6

COMMENTS

The A15 packing is the union of 8 translates of the lattice 4Z^3 by the vectors (0,0,0), (2,2,2) and all cyclic shifts of (0, +-1, 2).

LINKS

Table of n, a(n) for n=0..86.

Center for Computational Materials Science, Naval Research Laboratory (mehl(AT)dave.nrl.navy.mil), The A15 Structure

Encyclopedia of crystallographic prototypes, Cr_3Si (A15) Structure: A3B_cP8_223_c_a-001

Reticular Chemistry Structure Resource, bet

FORMULA

It seems that a(n) = A004013(n/4) + 12 * A045831((n-5)/8), where the terms with non-integer indices are set to 0. - Andrei Zabolotskii, Apr 15 2026

EXAMPLE

1 + 12*q^5 + 8*q^12 + 12*q^13 + 6*q^16 + 24*q^21 + 36*q^29 + 12*q^32 + ...

CROSSREFS

Cf. A063864.

Sequence in context: A083344 A294889 A308425 * A236238 A340362 A187795

Adjacent sequences: A063860 A063861 A063862 * A063864 A063865 A063866

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 27 2001

STATUS

approved