A003303 Numerators of spin-wave coefficients for cubic lattice. (Formerly M4672)

1, 9, 297, 7587, 1086939, 51064263, 5995159677, 423959714955, 281014370213715, 26702465299878195, 5723872792950096855, 682922353396120790085, 358992734790795421416975, 51516147618272668808063475

Offset

0,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Herman Jamke, Table of n, a(n) for n = 0..20

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

Formula

Let {g(n)} be the sequence of rational numbers defined by the recurrence: 256*(n+1)*g(n+1) - 32*(22*n^2+22n+9)*g(n) + 144*n*(4n^2+1)*g*(n-1) - 9*(2n-1)^4*g(n-2) = 0 (n>=0) with g(-2)=g(-1)=0 and g(1)=1. Then a(n) is the numerator of g(n). - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008

Prog

(PARI) g=vector(100); g[3]=1; print1("1, "); for(n=1, 30, g[n+3]=(32*(22*(n^2-n)+9)*g[n+2]-144*(n-1)*(4*(n-1)^2+1)*g[n+1]+9*(2*n-3)^4*g[n])/(256*n); print1(numerator(g[n+3])", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008

Crossrefs

Sequence in context: A027834 A175823 A129934 * A371252 A012838 A216966

Adjacent sequences: A003300 A003301 A003302 * A003304 A003305 A003306

Keyword

nonn,easy,frac

Author

N. J. A. Sloane

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008

Status

approved