A003284 Numerators of coefficients of Green function for cubic lattice. (Formerly M4777)

1, 1, 11, 19, 7861, 301259, 451526509, 6427914623, 16794274237, 12896029408223, 395798985324353, 30839190064680907, 164178854787337441961, 104746805369703910637, 30345665255129739404489

Offset

0,3

References

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.

G. S. Joyce, On the simple cubic lattice Green function, Phil. Trans. Roy. Soc., 273 (1972), 583-610.

Formula

Recurrence for the fraction A003284(n)/A003298(n) is the same as for A003299(n)/A003300(n). - R. J. Mathar, Dec 08 2005

36*n*(n+1)*(2n+1)*a(n+1)/A003298(n+1)-4*n*(20*n^2+1)*a(n)/A003298(n)+(2*n-1)^3*a(n-1)/A003298(n-1)=0. - R. J. Mathar, Dec 08 2005

Maple

Dnminus1 := 1 : print(numer(Dnminus1)) ; Dn := 1/18 : print(numer(Dn)) ; for nplus1 from 2 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 : # R. J. Mathar, Dec 08 2005

Crossrefs

Cf. A003298.

Sequence in context: A344431 A129909 A174976 * A257401 A283903 A063589

Adjacent sequences: A003281 A003282 A003283 * A003285 A003286 A003287

Keyword

nonn,easy,frac

Author

N. J. A. Sloane

Extensions

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

Status

approved