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A003300 Denominators of coefficients of Green function for cubic lattice.
(Formerly M5053)
3
1, 1, 18, 24, 27216, 5878656, 105815808, 346652587008, 693305174016, 299507835174912, 102431679629819904, 75255927891296256, 451535567347777536, 422637291037519773696, 479270688036547423371264 (list; graph; refs; listen; history; text; internal format)
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..14.

FORMULA

36*n*(n+1)*(2n+1)*A003299(n+1)/a(n+1)-4*n*(20*n^2+1)*A003299(n)/a(n)+(2*n-1)^3*A003299(n-1)/a(n-1) = 0. - R. J. Mathar, Dec 08 2005

MAPLE

print(1) ; Dnminus1 := 1 : print(denom(Dnminus1)) ; Dn := 7/18 : print(denom(Dn)) ; 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(denom(Dnplus1)) ; Dnminus1 := Dn : Dn := Dnplus1 : od : # R. J. Mathar

CROSSREFS

Cf. A003299.

Sequence in context: A109144 A166471 A072422 * A245022 A248111 A109769

Adjacent sequences:  A003297 A003298 A003299 * A003301 A003302 A003303

KEYWORD

nonn,easy,frac

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)