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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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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.
Sequence in context: A032642 A127633 A055246 this_sequence A006063 A038593 A014439
Adjacent sequences: A003279 A003280 A003281 this_sequence A003283 A003284 A003285
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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 17 2008
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