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A003281 Numerators of coefficients of Green function for cubic lattice.
(Formerly M5137)
1

%I M5137

%S 0,1,23,1477,555273,38466649,1711814393,48275151899,28127429172349,

%T 11820256380127,61330815490787739,1438084556561535649,

%U 3452174145433606905,1300912433743549667989,275638998008835888305243

%N Numerators of coefficients of Green function for cubic lattice.

%D G. S. Joyce, The simple cubic lattice Green function, Phil. Trans. Roy. Soc., 273 (1972), 583-610.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008, <a href="/A003281/b003281.txt">Table of n, a(n) for n = 0..22</a>

%F 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

%o (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

%K nonn,easy,frac

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 18 2008

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Last modified November 27 01:16 EST 2021. Contains 349344 sequences. (Running on oeis4.)