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A003303
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Numerators of spin-wave coefficients for cubic lattice.
(Formerly M4672)
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1
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1, 9, 297, 7587, 1086939, 51064263, 5995159677, 423959714955, 281014370213715, 26702465299878195, 5723872792950096855, 682922353396120790085, 358992734790795421416975, 51516147618272668808063475
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OFFSET
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0,2
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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).
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LINKS
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FORMULA
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Let {g(n)} be the sequence of rational numbers defined by the recurrence: 256*(n+1)*g(n+1) - 32*(22*n^2+22n+9)*g(n) + 144*n*(4n^2+1)*g*(n-1) - 9*(2n-1)^4*g(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
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008
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STATUS
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approved
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