|
Search: id:A003301
|
|
|
| A003301 |
|
Numerators of coefficients of Green function for cubic lattice.
(Formerly M1907)
|
|
+0
2
|
|
| 1, 2, 8, 496, 9088, 12032, 12004352, 4139008, 51347456, 378357612544, 4097254359040, 2921482158080, 9353679601664, 4929181267787776, 5689554887507968, 41627810786525052928, 37882178449895849984
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
G. S. Joyce, The simple cubic lattice Green function, Phil. Trans. Roy. Soc., 273 (1972), 583-610.
|
|
LINKS
|
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 (mathar(AT)strw.leidenuniv.nl), 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 : (Mathar)
|
|
CROSSREFS
|
Cf. A003302.
Sequence in context: A014185 A009808 A035129 this_sequence A000890 A033542 A098870
Adjacent sequences: A003298 A003299 A003300 this_sequence A003302 A003303 A003304
|
|
KEYWORD
|
nonn,easy,frac
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 08 2005
|
|
|
Search completed in 0.002 seconds
|
