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Search: id:A003283
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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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+0
2
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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; listen)
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OFFSET
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0,2
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REFERENCES
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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.
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FORMULA
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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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PROGRAM
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(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
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Cf. A003282.
Sequence in context: A133217 A001504 A136905 this_sequence A135188 A161007 A098077
Adjacent sequences: A003280 A003281 A003282 this_sequence A003284 A003285 A003286
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KEYWORD
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nonn,easy,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008
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