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Search: id:A005927
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| A005927 |
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Theta series of diamond with respect to deep hole.
(Formerly M3262)
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+0
2
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| 0, 0, 0, 4, 6, 0, 0, 0, 0, 0, 0, 12, 8, 0, 0, 0, 0, 0, 0, 12, 24, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 24, 30, 0, 0, 0, 0, 0, 0, 12, 24, 0, 0, 0, 0, 0, 0, 24, 24, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 12, 48, 0, 0, 0, 0, 0, 0, 28, 24, 0, 0, 0, 0, 0, 0, 36, 48, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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N. J. A. Sloane, Theta series and magic numbers for diamond and certain ionic crystal structures, J. Math. Phys. 28 (1987), 1653-1657.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
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Expansion of 4 * q^3 * psi^3(q^8) + (phi^3(q^4) - phi^3(-q^4)) / 2 in powers of q where phi(), psi() are Ramanujan theta functions. - Michael Somos Aug 17 2009
a(8*n + 0) = a(8*n + 1) = a(8*n + 2) = a(8*n + 5) = a(8*n + 6) = a(8*n + 7) = 0. - Michael Somos Aug 17 2009
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EXAMPLE
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4*q^3 + 6*q^4 + 12*q^11 + 8*q^12 + 12*q^19 + 24*q^20 + 16*q^27 + ... - Michael Somos Aug 17 2009
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PROGRAM
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(PARI) {a(n) = if( n<0, 0, if( n%8 == 3, n \= 8; polcoeff( 4 * sum(k=0, (sqrtint(8*n+1)-1)\2, x^((k^2+k)/2), x*O(x^n))^3, n), if( n%8 == 4, n /= 4; polcoeff( sum(k=1, sqrtint(n), 2*x^k^2, 1 + x*O(x^n))^3, n), 0 )))} /* Michael Somos Aug 17 2009 */
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CROSSREFS
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4 * A008443(n) = a(8*n + 3). A005887(n) = a(8*n + 4). - Michael Somos Aug 17 2009
Sequence in context: A134463 A058916 A064612 this_sequence A079207 A056945 A070683
Adjacent sequences: A005924 A005925 A005926 this_sequence A005928 A005929 A005930
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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