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A003283
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Denominators of coefficients of Green's function for cubic lattice.
(Formerly M2116)
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1
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1, 2, 20, 70, 112, 352, 1232, 22880, 183040, 1244672, 30098432, 72352, 2472371200, 115763200, 441223168, 6838959104, 61568122880, 745298329600, 28321336524800, 1103041527808, 573581594460160, 4275790067793920, 49961677422592
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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).
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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 denominator of C(n) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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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(denominator(C[n+3])", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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CROSSREFS
| Cf. A003282.
Sequence in context: A192351 A136905 A183907 * A135188 A161007 A098077
Adjacent sequences: A003280 A003281 A003282 * A003284 A003285 A003286
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KEYWORD
| nonn,easy,frac
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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