A003301 Numerators of coefficients of Green function for cubic lattice. (Formerly M1907)

1, 2, 8, 496, 9088, 12032, 12004352, 4139008, 51347456, 378357612544, 4097254359040, 2921482158080, 9353679601664, 4929181267787776, 5689554887507968, 41627810786525052928, 37882178449895849984

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..16.

G. S. Joyce and R. T. Delves, Exact product forms for the simple cubic lattice Green function: I, J Phys A: Math Gen 37 (2004) 3645-3671

Formula

9(n+1)(2n+1)(2n+3)*a(n+1)/A003302(n+1)-2(2n+1)(10n^2+10n+3)a(n)/A003302(n)+4n^3*a(n-1)/A003302(n-1) = 0. - R. J. Mathar, Dec 08 2005

Maple

Dnminus1 := 1 : print(numer(Dnminus1)) ; Dn := 2/9 : print(numer(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(numer(Dnplus1)) ; Dnminus1 := Dn : Dn := Dnplus1 : od : # R. J. Mathar

Crossrefs

Cf. A003302.

Sequence in context: A284603 A329685 A323863 * A000890 A033542 A098870

Adjacent sequences: A003298 A003299 A003300 * A003302 A003303 A003304

Keyword

nonn,easy,frac

Author

N. J. A. Sloane

Extensions

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

Status

approved