A371991 Number of different closest packings of equal spheres for hexagonal crystals having repeat period n.

1, 1, 0, 1, 1, 2, 3, 6, 6, 16, 21, 42, 63, 129, 201, 404, 685, 1340, 2385, 4625, 8487, 16409, 30735, 59282, 112530, 217182, 415605, 803076, 1545463, 2990945, 5778267, 11201472, 21702645, 42140890, 81830744, 159139428, 309590883, 602935713, 1174779207, 2290915478, 4469734225, 8726815041, 17047041429, 33319598126

Offset: 1

Author

R. J. Mathar, Apr 15 2024

Keywords

• nonn

Links

• J. E. Iglesias, A formula for the number of closest packings of equal spheres having a given repeat period, Z. Krist. 155 (1981) 121-127, Table 1.

Crossrefs

Cf. A000046, A371992.

Programs

PARI

apply( {A371991(n)=A000046(n)-A371992(n)}, [1..40]) \\ M. F. Hasler, Jun 09 2025

Formula

a(n) + A371992(n) = A000046(n).

a(n+1)/a(n) = 2 - 2/n + O(1/n^2). - M. F. Hasler, Jun 09 2025

Extensions

Offset changed to 1 and a(1) = 1 prefixed by M. F. Hasler, Jun 09 2025