A268244 - OEIS

%I #10 Jan 30 2016 13:00:04

%S 1,5,29,113,417,1325,3903,10611,26992,65102,148760,326638,686687,

%T 1398339,2748667,5261985,9784309,17789319,31564911,54933111,93643702,

%U 156953854,258427234,419200178,669550440,1055313420,1640871008,2521204924,3827438242,5748603482,8541662002,12569462958,18318439505

%N G.f.: (1 + x + 3*x^2 + 11*x^3 + 6*x^4 + 14*x^5 + 12*x^6 + 4*x^7 + 14*x^8 + 4*x^9 + 12*x^10 + 14*x^11 + 5*x^ 12 + 11*x^13 + 9*x^14 - 11*x^15)/((1 - x)^4*(1 - x^2)^12).

%C The formula on page 194 of Benson (1987) has at least two errors. This is my best guess as what was intended. This is supposed to be the growth series for the three-dimensional upper triangular matrix group.

%D Benson, Max. "On the rational growth of virtually nilpotent groups" in Annals of Mathematics Studies 111 (1987): 185-196, edited by Gersten, Stephen M., and John Robert Stallings. See page 194.

%p f0:=[1,1,3,11,6,14,12,4,14,4,12,14,5,11,9,-11];

%p f1:=add(f0[i]*x^(i-1),i=1..nops(f0));

%p f2:=f1/((1-x)^4*(1-x^2)^12);

%p series(f2,x,40);

%p seriestolist(%);

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jan 30 2016