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A005872
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Theta series of hexagonal close-packing with respect to octahedral hole.
(Formerly M4040)
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5
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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
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OFFSET
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0,4
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REFERENCES
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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.
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LINKS
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FORMULA
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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 */
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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