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Search: id:A003302
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| A003302 |
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Denominators of coefficients of Green function for cubic lattice.
(Formerly M4655)
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+0
2
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| 1, 9, 81, 8505, 229635, 413343, 531972441, 227988189, 3419822835, 29824274944035, 375785864294841, 307461161695779, 1116569481947829, 660923243352964935, 849758455739526345, 6875395665388507657395
(list; graph; listen)
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OFFSET
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0,2
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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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9(n+1)(2n+1)(2n+3)A003301(n+1)/a(n+1)-2(2n+1)(10n^2+10n+3)A003301(n)/a(n)+4n^3A003301(n-1)/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(denom(Dnminus1)) ; Dn := 2/9 : print(denom(Dn)) ; for nplus1 from 2 to 20 do n := nplus1-1 : Dnplus1 := (2*(2*n+1)*(10*n^2+10*n+3)*Dn-4*n^3*Dnminus1)/(9*nplus1*(2*n+1)*(2*n+3)) : print(denom(Dnplus1)) ; Dnminus1 := Dn : Dn := Dnplus1 : od : (Mathar)
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CROSSREFS
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Cf. A003301.
Adjacent sequences: A003299 A003300 A003301 this_sequence A003303 A003304 A003305
Sequence in context: A061433 A069659 A110853 this_sequence A053915 A067216 A076088
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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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