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A003282 Numerators of coefficients of Green function for cubic lattice.
(Formerly M4360)
1
1, 1, 7, 19, 25, 67, 205, 3389, 24469, 151805, 3378595, 7529, 239951407, 10532699, 37801901, 553870985, 4729453873, 54466083977, 1974303293437, 73525821439, 36638106109621, 262239579597193, 2947415049407, 90871116596785 (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..23.

FORMULA

Let C(n) be the sequence of rational numbers defined by the recurrence: 8(n+1)(2n+1)(2n+3)C(n+1)-6(2n+1)(5n^2+5n+2)C(n)+24n^3C(n-1)+2n(n-1)(2n-1)C(n-2)=0 n>=0 with C(0)=1 and C(n)=0 if n<0. Then a(n) is the numerator of C(n) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008

PROG

(PARI) C=vector(100); C[3]=1; print1(C[3]", "); for(n=1, 30, C[n+3]=(6*(2*n-1)*(5*n^2-5*n+2)*C[n+2]-24*(n-1)^3*C[n+1]-2*(n-1)*(n-2)*(2*n-3)*C[n])/(8*n*(2*n-1)*(2*n+1)); print1(numerator(C[n+3])", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008

CROSSREFS

Cf. A003283.

Sequence in context: A032642 A127633 A055246 * A006063 A181123 A038593

Adjacent sequences:  A003279 A003280 A003281 * A003283 A003284 A003285

KEYWORD

nonn,easy,frac

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008

STATUS

approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)