A217512 Partial sums of nonzero terms in A005925.

1, 5, 17, 29, 35, 47, 71, 87, 99, 123, 147, 159, 167, 191, 239, 275, 281, 293, 329, 357, 381, 417, 441, 465, 489, 525, 597, 633, 657, 705, 729, 741, 801, 849, 885, 915, 943, 1015, 1063, 1087, 1099, 1147, 1207, 1231, 1291, 1339, 1363, 1371, 1419, 1503, 1551

Offset

0,2

Comments

Sizes of clusters of atoms in diamond structure.

References

N. J. A. Sloane, Theta-Series and Magic Numbers for Diamond and Certain Ionic Crystal Structures, J. Math. Phys., 28 (1987), pp. 1653-1657.

Links

Table of n, a(n) for n=0..50.

Prog

(PARI) lista(m) = {nm = sqrtint(m)+1; T2 = sum(i=0, nm, 2*x^((i+1/2)^2 - 1/4)); T23 = T2^3; T3 = 1+ sum(i=1, nm, 2*x^(i^2)); T4 = subst(T3, x, -x); T33 = T3^3; T334 = sum(i=0, m, polcoeff(T33, i)*x^(4*i)); T43 = T4^3; T434 = sum(i=0, m, polcoeff(T43, i)*x^(4*i)); P = sum(i=0, poldegree(T23), polcoeff(T23, i)*x^(numerator(i+3/4))); D = (P + T334 + T434)/2; s = 0; for (i=0, m, v = polcoeff(D, i); if (v != 0, s += v; print1(s, ", "); ); ); } \\ Michel Marcus, Feb 19 2013

Crossrefs

Cf. A005925-A005927, A217512-A217514.

Sequence in context: A195032 A264618 A271471 * A289836 A068829 A090403

Adjacent sequences: A217509 A217510 A217511 * A217513 A217514 A217515

Keyword

nonn

Author

N. J. A. Sloane, Oct 05 2012

Extensions

More terms from Michel Marcus, Feb 19 2013

Status

approved