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 A005872 Theta series of hexagonal close-packing with respect to octahedral hole. (Formerly M4040) 4
 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 12, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 18, 0, 0, 0, 0, 0, 12, 0, 12, 0, 0, 0, 24, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 24, 0, 0, 0, 0, 0, 24, 0, 6, 0, 0, 0, 36, 0, 12, 0, 0, 0, 0, 0, 12, 0, 0, 0, 30, 0, 0, 0, 0, 0, 18 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). N. J. A. Sloane and B. K. Teo, Theta series and magic numbers for close-packed spherical clusters, J. Chem. Phys. 83 (1985) 6520-6534. LINKS Sean A. Irvine, Table of n, a(n) for n = 0..999 FORMULA a(2*n) = 0. a(2*n + 3) = 6*A298931(n). - Michael Somos, Jul 06 2018 EXAMPLE G.f. = 6*q^3 + 6*q^9 + 6*q^11 + 12*q^15 + 6*q^17 + 12*q^23 + 18*q^27 + ... - Michael Somos, Jul 06 2018 MATHEMATICA a[ n_] := SeriesCoefficient[ 6 x^3 QPochhammer[ x^16]^2 QPochhammer[ x^18]^3 / (QPochhammer[ x^6] QPochhammer[ x^8]), {x, 0, n}]; (* Michael Somos, Jul 06 2018 *) PROG (PARI) {a(n) = my(A, m); if( n<3 || n%2==0, 0, m = n\2 - 1; A = x * O(x^m); 6 * polcoeff( eta(x^8 + A)^2 * eta(x^9 + A)^3 / (eta(x^3 + A) * eta(x^4 + A)), m))}; /* Michael Somos, Jul 06 2018 */ CROSSREFS Cf. A298931. Sequence in context: A187794 A200214 A294887 * A035322 A270031 A284105 Adjacent sequences:  A005869 A005870 A005871 * A005873 A005874 A005875 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified January 16 23:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)