Search: id:A003303
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%I A003303 M4672
%S A003303 1,9,297,7587,1086939,51064263,5995159677,423959714955,281014370213715,
%T A003303 26702465299878195,5723872792950096855,682922353396120790085,
%U A003303 358992734790795421416975,51516147618272668808063475
%N A003303 Numerators of spin-wave coefficients for cubic lattice.
%D A003303 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003303 G. S. Joyce, The simple cubic lattice Green function, Phil. Trans. Roy. 
               Soc., 273 (1972), 583-610.
%H A003303 Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008, <a href="b003303.txt">
               Table of n, a(n) for n = 0..20</a>
%F A003303 Let g(n) be the sequence of rational numbers defined by the recurrence: 
               256(n+1)g(n+1)-32(22n^2+22n+9)g(n)+144n(4n^2+1)g(n-1)-9(2n-1)^4g(n-2)=0 
               (n>=0) with g(-2)=g(-1)=0 and g(1)=1. Then a(n) is the numerator 
               of g(n) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008
%o A003303 (PARI) g=vector(100);g[3]=1;print1("1,");for(n=1,30,g[n+3]=(32*(22*(n^2-n)+9)*g[n+2]-144*(n-1)*(4*(n-1)^2+1)*\
               g[n+1]+9*(2*n-3)^4*g[n])/(256*n);print1(numerator(g[n+3])",")) - 
               Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008
%Y A003303 Sequence in context: A086699 A027834 A129934 this_sequence A012838 A061685 
               A104775
%Y A003303 Adjacent sequences: A003300 A003301 A003302 this_sequence A003304 A003305 
               A003306
%K A003303 nonn,easy,frac
%O A003303 0,2
%A A003303 N. J. A. Sloane (njas(AT)research.att.com).
%E A003303 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008

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