A003281 Numerators of coefficients of Green function for cubic lattice. (Formerly M5137)

0, 1, 23, 1477, 555273, 38466649, 1711814393, 48275151899, 28127429172349, 11820256380127, 61330815490787739, 1438084556561535649, 3452174145433606905, 1300912433743549667989, 275638998008835888305243

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

Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008, Table of n, a(n) for n = 0..22

Formula

Let {B1(n)} be the sequence of rational numbers defined by the recurrence: 16*n*(n+1)*(2n+1)*B1(n+1) - n*(60n^2+9)*B1(n) + 3*(2n-1)^3*B1(n-1) + (n-1)*(2n-1)*(2n-3)*B1(n-2) = 0 for n >= 1 with B1(0) = 0 and B1(1) = 1. Then a(n) is the numerator of B1(n). - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008

Prog

(PARI) B1=vector(100); B1[4]=1; print1("0, 1, "); for(n=2, 30, B1[n+3]=((n-1)*(60*(n-1)^2+9)*B1[n+2]-3*(2*n-3)^3*B1[n+1]-(n-2)*(2*n-3)*(2*n-5)*B1[n])/(16*(n-1)*n*(2*n-1)); print1(numerator(B1[n+3])", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008

Crossrefs

Sequence in context: A351508 A248703 A264903 * A330658 A034243 A183480

Adjacent sequences: A003278 A003279 A003280 * A003282 A003283 A003284

Keyword

nonn,easy,frac

Author

N. J. A. Sloane

Extensions

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

Status

approved