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A003281
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Numerators of coefficients of Green function for cubic lattice.
(Formerly M5137)
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1
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0, 1, 23, 1477, 555273, 38466649, 1711814393, 48275151899, 28127429172349, 11820256380127, 61330815490787739, 1438084556561535649, 3452174145433606905, 1300912433743549667989, 275638998008835888305243
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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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LINKS
| Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008, Table of n, a(n) for n = 0..22
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FORMULA
| 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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PROG
| (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
| Sequence in context: A201309 A049003 A196422 * A034243 A183480 A002439
Adjacent sequences: A003278 A003279 A003280 * A003282 A003283 A003284
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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 18 2008
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