A003302 Denominators of coefficients of Green function for cubic lattice. (Formerly M4655)

1, 9, 81, 8505, 229635, 413343, 531972441, 227988189, 3419822835, 29824274944035, 375785864294841, 307461161695779, 1116569481947829, 660923243352964935, 849758455739526345, 6875395665388507657395

Offset

0,2

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).

Links

Table of n, a(n) for n=0..15.

Formula

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, Dec 08 2005

Maple

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 : # R. J. Mathar

Crossrefs

Cf. A003301.

Sequence in context: A167723 A203107 A168493 * A053915 A067216 A076088

Adjacent sequences: A003299 A003300 A003301 * A003303 A003304 A003305

Keyword

nonn,easy,frac

Author

N. J. A. Sloane

Extensions

More terms from R. J. Mathar, Dec 08 2005

Status

approved