A003300 Denominators of coefficients of Green function for cubic lattice. (Formerly M5053)

1, 1, 18, 24, 27216, 5878656, 105815808, 346652587008, 693305174016, 299507835174912, 102431679629819904, 75255927891296256, 451535567347777536, 422637291037519773696, 479270688036547423371264

Offset

0,3

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..14.

Formula

36*n*(n+1)*(2n+1)*A003299(n+1)/a(n+1)-4*n*(20*n^2+1)*A003299(n)/a(n)+(2*n-1)^3*A003299(n-1)/a(n-1) = 0. - R. J. Mathar, Dec 08 2005

Maple

print(1) ; Dnminus1 := 1 : print(denom(Dnminus1)) ; Dn := 7/18 : print(denom(Dn)) ; 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(denom(Dnplus1)) ; Dnminus1 := Dn : Dn := Dnplus1 : od : # R. J. Mathar

Crossrefs

Cf. A003299.

Sequence in context: A109144 A166471 A072422 * A245022 A362435 A248111

Adjacent sequences: A003297 A003298 A003299 * A003301 A003302 A003303

Keyword

nonn,easy,frac

Author

N. J. A. Sloane

Extensions

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

Status

approved