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Search: id:A003303
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| A003303 |
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Numerators of spin-wave coefficients for cubic lattice.
(Formerly M4672)
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+0
1
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| 1, 9, 297, 7587, 1086939, 51064263, 5995159677, 423959714955, 281014370213715, 26702465299878195, 5723872792950096855, 682922353396120790085, 358992734790795421416975, 51516147618272668808063475
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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G. S. Joyce, The simple cubic lattice Green function, Phil. Trans. Roy. Soc., 273 (1972), 583-610.
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LINKS
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Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008, Table of n, a(n) for n = 0..20
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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(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
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PROGRAM
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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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Sequence in context: A086699 A027834 A129934 this_sequence A012838 A061685 A104775
Adjacent sequences: A003300 A003301 A003302 this_sequence A003304 A003305 A003306
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KEYWORD
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nonn,easy,frac
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AUTHOR
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njas
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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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