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Search: id:A003281
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| A003281 |
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Numerators of coefficients of Green function for cubic lattice.
(Formerly M5137)
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+0
1
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| 0, 1, 23, 1477, 555273, 38466649, 1711814393, 48275151899, 28127429172349, 11820256380127, 61330815490787739, 1438084556561535649, 3452174145433606905, 1300912433743549667989, 275638998008835888305243
(list; graph; listen)
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OFFSET
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0,3
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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..22
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FORMULA
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Let B1(n) be the sequence of rational numbers defined by the recurrence: 16n(n+1)(2n+1)B1(n+1)-n(60n^2+9)B1(n)+3(2n-1)^3B1(n-1)+(n-1)(2n-1)(2n-3)B1(n-2)=0 n>=1 with B1(0)=0 and B1(1)=1. Then a(n) is the numerator of B1(n) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008
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PROGRAM
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(PARI) B1=vector(100); B1[4]=1; print1("0, 1, "); for(n=2, 30, B1[n+3]=((n-1)*(60*(n-1)^2+9)*B1[n+2]-3*(2*n-3)^3*B1[n+1]-(n-2)*(2*n-3)*(2*n-5)*\ B1[n])/(16*(n-1)*n*(2*n-1)); print1(numerator(B1[n+3])", ")) - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008
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CROSSREFS
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Sequence in context: A061063 A100768 A049003 this_sequence A034243 A002439 A132395
Adjacent sequences: A003278 A003279 A003280 this_sequence A003282 A003283 A003284
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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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