A005926 -id:A005926 - cp's OEIS frontend

A217513 Partial sums of nonzero terms in A005926.

2, 8, 20, 32, 38, 56, 74, 86, 116, 130, 136, 166, 190, 208, 238, 264, 288, 318, 342, 360, 384, 420, 444, 492, 522, 534, 588, 612, 648, 690, 714, 732, 768, 822, 840, 894, 942, 966, 1026, 1050, 1068, 1134, 1190, 1220, 1256, 1280, 1310, 1382, 1418, 1448, 1508

Offset: 0

N. J. A. Sloane, Oct 05 2012

nonn

Sizes of clusters of atoms in diamond structure.

Andy Huchala, Table of n, a(n) for n = 0..98
N. J. A. Sloane, Theta series and magic numbers for diamond and certain ionic crystal structures, J. Math. Phys. 28 (1987), 1653-1657.

Cf. A005925-A005927, A217512-A217514.

More terms from Andy Huchala, May 17 2023

A045840 a(n) = A005926(n)/2.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6

Offset: 0

N. J. A. Sloane

nonn

Antti Karttunen, Table of n, a(n) for n = 0..387 (computed from b-file of A005926 provided by Herman Jamke)

Cf. A005926.

More terms (computed from those of A005926) by Antti Karttunen, Jul 24 2017

A005925 Theta series of diamond.

Original entry on oeis.org

1, 0, 0, 4, 0, 0, 0, 0, 12, 0, 0, 12, 0, 0, 0, 0, 6, 0, 0, 12, 0, 0, 0, 0, 24, 0, 0, 16, 0, 0, 0, 0, 12, 0, 0, 24, 0, 0, 0, 0, 24, 0, 0, 12, 0, 0, 0, 0, 8, 0, 0, 24, 0, 0, 0, 0, 48, 0, 0, 36, 0, 0, 0, 0, 6, 0, 0, 12

Offset: 0

N. J. A. Sloane

a(n) > 0 iff n is in A047470. - Robert Israel, Jul 06 2016

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Robert Israel, Table of n, a(n) for n = 0..10000
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, p. 120.
G. L. Hall, Comment on the paper "Theta series and magic numbers for diamond and certain ionic crystal structures" [J. Math. Phys. 28, 1653 (1987)]. Journal of Mathematical Physics; Sep. 1988, Vol. 29 Issue 9, pp. 2090-2092. - From _N. J. A. Sloane_, Dec 18 2012
N. J. A. Sloane, Theta series and magic numbers for diamond and certain ionic crystal structures, J. Math. Phys. 28 (1987), 1653-1657.

Cf. A005926, A005927, A047470, A217512, A217513, A217514.

S:= series((JacobiTheta2(0,z^4)^3 + JacobiTheta3(0,z^4)^3 + JacobiTheta4(0,z^4)^3)/2, z, 101):
seq(coeff(S,z,j),j=0..100); # Robert Israel, Jul 06 2016

terms = 68; s = Simplify[Normal[(EllipticTheta[2, 0, z^4]^3 + EllipticTheta[3, 0, z^4]^3 + EllipticTheta[4, 0, z^4]^3)/2 + O[z]^terms], z > 0]; CoefficientList[s, z] (* Jean-François Alcover, Jul 07 2017 *)

(theta_2^3 + theta_3^3 + theta_4^3) / 2.

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A217513 Partial sums of nonzero terms in A005926.

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A045840 a(n) = A005926(n)/2.

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A005925 Theta series of diamond.

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