A003299 Numerators of coefficients of Green function for cubic lattice. (Formerly M4331)

0, 1, 7, 5, 3635, 557485, 7596391, 19681954039, 32139541115, 11613832153165, 3386240626860905, 2153823021586357, 11330361348611303, 9397464146366084237, 9528720716522267278849, 309116925259099828695359

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

Table of n, a(n) for n=0..15.

Formula

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

Maple

Dnminus1 := 1 : print(numer(Dnminus1)) ; Dn := 7/18 : print(numer(Dn)) ; n := 2 : for nplus1 from 3 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

Crossrefs

Cf. A003300.

Sequence in context: A300452 A302201 A263171 * A198677 A154017 A100222

Adjacent sequences: A003296 A003297 A003298 * A003300 A003301 A003302

Keyword

nonn,easy,frac

Author

N. J. A. Sloane

Extensions

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

Status

approved