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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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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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Adjacent sequences: A003300 A003301 A003302 this_sequence A003304 A003305 A003306
Sequence in context: A086699 A027834 A129934 this_sequence A012838 A061685 A104775
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KEYWORD
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nonn,easy,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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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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