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Search: id:A005887
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| A005887 |
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Theta series of f.c.c. lattice with respect to octahedral hole.
(Formerly M4070)
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+0
4
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| 6, 8, 24, 0, 30, 24, 24, 0, 48, 24, 48, 0, 30, 32, 72, 0, 48, 48, 24, 0, 96, 24, 72, 0, 54, 48, 72, 0, 48, 72, 72, 0, 96, 24, 96, 0, 48, 56, 96, 0, 102, 72, 48, 0, 144, 48, 48, 0, 48, 72, 168, 0, 96, 72, 72, 0, 96, 48, 120, 0, 78, 48, 144, 0, 144, 120, 48, 0, 96, 72, 96, 0, 96, 56, 168
(list; graph; listen)
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OFFSET
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0,1
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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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N. J. A. Sloane, Table of n, a(n) for n = 0..9999
G. Nebe and N. J. A. Sloane, Home page for this lattice
Index entries for sequences related to f.c.c. lattice
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FORMULA
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Expansion of q^(-1) * (phi^3(q) - phi^3(-q)) / 2 in powers of q^2 where phi() is a Ramanujan theta function. - Michael Somos Aug 17 2009
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EXAMPLE
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6*q + 8*q^3 + 24*q^5 + 30*q^9 + 24*q^11 + 24*q^13 + 48*q^17 + 24*q^19 + ... - Michael Somos Aug 17 2009
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MAPLE
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maxd:=20001: read format: temp0:=trunc(evalf(sqrt(maxd)))+2: a:=0: for i from -temp0 to temp0 do a:=a+q^( (i+1/2)^2): od: th2:=series(a, q, maxd): a:=0: for i from -temp0 to temp0 do a:=a+q^(i^2): od: th3:=series(a, q, maxd): th4:=series(subs(q=-q, th3), q, maxd):
t1:=series((th3^3-th4^3)/(2*q), q, maxd): t1:=series(subs(q=sqrt(q), t1), q, floor(maxd/2)): t2:=seriestolist(t1): for n from 1 to nops(t2) do lprint(n-1, t2[n]); od:
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PROGRAM
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(PARI) {a(n) = if( n<0, 0, n = 2*n + 1; polcoeff( sum(k=1, sqrtint(n), 2*x^k^2, 1 + x*O(x^n))^3, n))} /* Michael Somos */
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CROSSREFS
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A005875(2*n + 1) = A(n). - Michael Somos Aug 17 2009
Adjacent sequences: A005884 A005885 A005886 this_sequence A005888 A005889 A005890
Sequence in context: A024868 A034761 A085796 this_sequence A119875 A053189 A156231
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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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