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A003284
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Numerators of coefficients of Green function for cubic lattice.
(Formerly M4777)
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2
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1, 1, 11, 19, 7861, 301259, 451526509, 6427914623, 16794274237, 12896029408223, 395798985324353, 30839190064680907, 164178854787337441961, 104746805369703910637, 30345665255129739404489
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| G. S. Joyce, The simple cubic lattice Green function, Phil. Trans. Roy. Soc., 273 (1972), 583-610.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| Recurrence for the fraction A003284(n)/A003298(n) is the same as for A003299(n)/A003300(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 08 2005
36*n*(n+1)*(2n+1)*a(n+1)/A003298(n+1)-4*n*(20*n^2+1)*a(n)/A003298(n)+(2*n-1)^3*a(n-1)/A003298(n-1)=0 - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 08 2005
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MAPLE
| Dnminus1 := 1 : print(numer(Dnminus1)) ; Dn := 1/18 : print(numer(Dn)) ; for nplus1 from 2 to 20 do n := nplus1-1 : Dnplus1 := (4*n*(20*n^2+1)*Dn-(2*n-1)^3*Dnminus1)/(36*n*nplus1*(2*n+1)) : print(numer(Dnplus1)) ; Dnminus1 := Dn : Dn := Dnplus1 : od : (Mathar)
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CROSSREFS
| Cf. A003298.
Sequence in context: A129908 A129909 A174976 * A063589 A102815 A105957
Adjacent sequences: A003281 A003282 A003283 * A003285 A003286 A003287
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KEYWORD
| nonn,easy,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 08 2005
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