A003283 Denominators of coefficients of Green function for cubic lattice. (Formerly M2116)

1, 2, 20, 70, 112, 352, 1232, 22880, 183040, 1244672, 30098432, 72352, 2472371200, 115763200, 441223168, 6838959104, 61568122880, 745298329600, 28321336524800, 1103041527808, 573581594460160, 4275790067793920, 49961677422592

Offset

0,2

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..22.

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 denominator 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(denominator(C[n+3])", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008

Crossrefs

Cf. A003282.

Sequence in context: A216609 A226394 A287485 * A259110 A135188 A161007

Adjacent sequences: A003280 A003281 A003282 * A003284 A003285 A003286

Keyword

nonn,easy,frac

Author

N. J. A. Sloane

Extensions

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

Status

approved