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A003283 Denominators of coefficients of Green's function for cubic lattice.
(Formerly M2116)
1

%I M2116

%S 1,2,20,70,112,352,1232,22880,183040,1244672,30098432,72352,

%T 2472371200,115763200,441223168,6838959104,61568122880,745298329600,

%U 28321336524800,1103041527808,573581594460160,4275790067793920,49961677422592

%N Denominators of coefficients of Green's 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).

%F 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

%o (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

%Y Cf. A003282.

%K nonn,easy,frac

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 17 2008

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Last modified January 25 19:00 EST 2022. Contains 350572 sequences. (Running on oeis4.)