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Search: id:A003280
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| A003280 |
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Numerators of coefficients of Green function for cubic lattice.
(Formerly M4664)
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+0
1
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| 1, 9, 175, 2025, 102235, 1356047, 37160123, 6771931925, 772428184055, 189690563847015, 105217453376898775, 1548913291275244825, 2112565685454158552975, 1658173107161491979625
(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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LINKS
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Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008, Table of n, a(n) for n = 0..23
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FORMULA
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Let B0(n) be the sequence of rational numbers defined by the recurrence: 16n(n+1)(2n+1)B0(n+1)-n(60n^2+9)B0(n)+3(2n-1)^3B0(n-1)+(n-1)(2n-1)(2n-3)B0(n-2)=0 n>=1 with B0(0)=1 and B0(1)=9/32. Then a(n) is the numerator of B0(n) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008
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PROGRAM
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(PARI) B0=vector(100); B0[3]=1; B0[4]=9/32; print1("1, 9, "); for(n=2, 30, B0[n+3]=((n-1)*(60*(n-1)^2+9)*B0[n+2]-3*(2*n-3)^3*B0[n+1]-(n-2)*(2*n-3)*(2*n-5)*\ B0[n])/(16*(n-1)*n*(2*n-1)); print1(numerator(B0[n+3])", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008
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CROSSREFS
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Sequence in context: A049212 A141441 A027956 this_sequence A141359 A141363 A157774
Adjacent sequences: A003277 A003278 A003279 this_sequence A003281 A003282 A003283
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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 18 2008
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