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Search: id:A003282
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| A003282 |
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Numerators of coefficients of Green function for cubic lattice.
(Formerly M4360)
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+0
2
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| 1, 1, 7, 19, 25, 67, 205, 3389, 24469, 151805, 3378595, 7529, 239951407, 10532699, 37801901, 553870985, 4729453873, 54466083977, 1974303293437, 73525821439, 36638106109621, 262239579597193, 2947415049407, 90871116596785
(list; graph; listen)
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OFFSET
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0,3
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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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FORMULA
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Let C(n) be the sequence of rational numbers defined by the recurrence: 8(n+1)(2n+1)(2n+3)C(n+1)-6(2n+1)(5n^2+5n+2)C(n)+24n^3C(n-1)+2n(n-1)(2n-1)C(n-2)=0 n>=0 with C(0)=1 and C(n)=0 if n<0. Then a(n) is the numerator of C(n) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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PROGRAM
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(PARI) C=vector(100); C[3]=1; print1(C[3]", "); for(n=1, 30, C[n+3]=(6*(2*n-1)*(5*n^2-5*n+2)*C[n+2]-24*(n-1)^3*C[n+1]-2*(n-1)*(n-2)*(2*n-3)*C\ [n])/(8*n*(2*n-1)*(2*n+1)); print1(numerator(C[n+3])", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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CROSSREFS
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Cf. A003283.
Adjacent sequences: A003279 A003280 A003281 this_sequence A003283 A003284 A003285
Sequence in context: A032642 A127633 A055246 this_sequence A006063 A038593 A014439
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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 17 2008
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