A003301 - OEIS

A003301

Numerators of coefficients of Green function for cubic lattice.
(Formerly M1907)

1, 2, 8, 496, 9088, 12032, 12004352, 4139008, 51347456, 378357612544, 4097254359040, 2921482158080, 9353679601664, 4929181267787776, 5689554887507968, 41627810786525052928, 37882178449895849984

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OFFSET

0,2

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..16.

G. S. Joyce and R. T. Delves, Exact product forms for the simple cubic lattice Green function: I, J Phys A: Math Gen 37 (2004) 3645-3671

FORMULA

9(n+1)(2n+1)(2n+3)*a(n+1)/A003302(n+1)-2(2n+1)(10n^2+10n+3)a(n)/A003302(n)+4n^3*a(n-1)/A003302(n-1) = 0. - R. J. Mathar, Dec 08 2005

MAPLE

Dnminus1 := 1 : print(numer(Dnminus1)) ; Dn := 2/9 : print(numer(Dn)) ; for nplus1 from 2 to 20 do n := nplus1-1 : Dnplus1 := (2*(2*n+1)*(10*n^2+10*n+3)*Dn-4*n^3*Dnminus1)/(9*nplus1*(2*n+1)*(2*n+3)) : print(numer(Dnplus1)) ; Dnminus1 := Dn : Dn := Dnplus1 : od : # R. J. Mathar

CROSSREFS

Cf. A003302.

Sequence in context: A284603 A329685 A323863 * A000890 A033542 A098870

Adjacent sequences: A003298 A003299 A003300 * A003302 A003303 A003304

KEYWORD

nonn,easy,frac

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved