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Search: id:A003299
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| A003299 |
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Numerators of coefficients of Green function for cubic lattice.
(Formerly M4331)
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+0
4
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| 0, 1, 7, 5, 3635, 557485, 7596391, 19681954039, 32139541115, 11613832153165, 3386240626860905, 2153823021586357, 11330361348611303, 9397464146366084237, 9528720716522267278849, 309116925259099828695359
(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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36*n*(n+1)*(2*n+1)*a(n+1)-4*n*(20*n^2+1)*a(n)+(2*n-1)^3*a(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 := 7/18 : print(numer(Dn)) ; n := 2 : for nplus1 from 3 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. A003300.
Adjacent sequences: A003296 A003297 A003298 this_sequence A003300 A003301 A003302
Sequence in context: A007553 A002019 A012878 this_sequence A100222 A011236 A111508
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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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