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Search: id:A003284
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| A003284 |
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Numerators of coefficients of Green function for cubic lattice.
(Formerly M4777)
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+0
2
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| 1, 1, 11, 19, 7861, 301259, 451526509, 6427914623, 16794274237, 12896029408223, 395798985324353, 30839190064680907, 164178854787337441961, 104746805369703910637, 30345665255129739404489
(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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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
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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
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Cf. A003298.
Sequence in context: A032370 A129908 A129909 this_sequence A063589 A102815 A105957
Adjacent sequences: A003281 A003282 A003283 this_sequence A003285 A003286 A003287
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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 R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 08 2005
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