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A003284 Numerators of coefficients of Green function for cubic lattice.
(Formerly M4777)
2
1, 1, 11, 19, 7861, 301259, 451526509, 6427914623, 16794274237, 12896029408223, 395798985324353, 30839190064680907, 164178854787337441961, 104746805369703910637, 30345665255129739404489 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

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.

G. S. Joyce, On the simple cubic lattice Green function, Phil. Trans. Roy. Soc., 273 (1972), 583-610.

FORMULA

Recurrence for the fraction A003284(n)/A003298(n) is the same as for A003299(n)/A003300(n). - R. J. Mathar, Dec 08 2005

36*n*(n+1)*(2n+1)*a(n+1)/A003298(n+1)-4*n*(20*n^2+1)*a(n)/A003298(n)+(2*n-1)^3*a(n-1)/A003298(n-1)=0. - R. J. Mathar, Dec 08 2005

MAPLE

Dnminus1 := 1 : print(numer(Dnminus1)) ; Dn := 1/18 : print(numer(Dn)) ; for nplus1 from 2 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, Dec 08 2005

CROSSREFS

Cf. A003298.

Sequence in context: A129908 A129909 A174976 * A257401 A283903 A063589

Adjacent sequences:  A003281 A003282 A003283 * A003285 A003286 A003287

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 January 19 17:45 EST 2019. Contains 319309 sequences. (Running on oeis4.)