Search: id:A005887
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%I A005887 M4070
%S A005887 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,
%T A005887 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,
%U A005887 0,96,72,72,0,96,48,120,0,78,48,144,0,144,120,48,0,96,72,96,0,96,56,168
%N A005887 Theta series of f.c.c. lattice with respect to octahedral hole.
%D A005887 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005887 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.
%H A005887 N. J. A. Sloane, <a href="b005887.txt">Table of n, a(n) for n = 0..9999</
               a>
%H A005887 G. Nebe and N. J. A. Sloane, <a href="http://www.research.att.com/~njas/
               lattices/D3.html">Home page for this lattice</a>
%H A005887 <a href="Sindx_Fa.html#fcc">Index entries for sequences related to f.c.c. 
               lattice</a>
%F A005887 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
%e A005887 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
%p A005887 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):
%p A005887 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:
%o A005887 (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 */
%Y A005887 A005875(2*n + 1) = A(n). - Michael Somos Aug 17 2009
%Y A005887 Sequence in context: A024868 A034761 A085796 this_sequence A119875 A053189 
               A156231
%Y A005887 Adjacent sequences: A005884 A005885 A005886 this_sequence A005888 A005889 
               A005890
%K A005887 nonn
%O A005887 0,1
%A A005887 N. J. A. Sloane (njas(AT)research.att.com).

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