A003282 Numerators of coefficients of Green function for cubic lattice. (Formerly M4360)

1, 1, 7, 19, 25, 67, 205, 3389, 24469, 151805, 3378595, 7529, 239951407, 10532699, 37801901, 553870985, 4729453873, 54466083977, 1974303293437, 73525821439, 36638106109621, 262239579597193, 2947415049407, 90871116596785

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..23.

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

Formula

Let {C(n)} be the sequence of rational numbers defined by the recurrence: 8*(n+1)*(2n+1)*(2n+3)*C(n+1) - 6*(2n+1)*(5n^2+5n+2)*C(n) + 24*n^3*C(n-1) + 2*n*(n-1)*(2n-1)*C(n-2) = 0 for n >= 0 with C(0) = 1 and C(n) = 0 if n < 0. Then a(n) is the numerator of C(n). - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008

Prog

(PARI) C=vector(100); C[3]=1; print1(C[3]", "); for(n=1, 30, C[n+3]=(6*(2*n-1)*(5*n^2-5*n+2)*C[n+2]-24*(n-1)^3*C[n+1]-2*(n-1)*(n-2)*(2*n-3)*C[n])/(8*n*(2*n-1)*(2*n+1)); print1(numerator(C[n+3])", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008

Crossrefs

Cf. A003283.

Sequence in context: A032642 A127633 A055246 * A006063 A181123 A038593

Adjacent sequences: A003279 A003280 A003281 * A003283 A003284 A003285

Keyword

nonn,easy,frac

Author

N. J. A. Sloane

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008

Status

approved