A268244 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).

1, 5, 29, 113, 417, 1325, 3903, 10611, 26992, 65102, 148760, 326638, 686687, 1398339, 2748667, 5261985, 9784309, 17789319, 31564911, 54933111, 93643702, 156953854, 258427234, 419200178, 669550440, 1055313420, 1640871008, 2521204924, 3827438242, 5748603482, 8541662002, 12569462958, 18318439505

Offset

0,2

Comments

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.

References

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.

Links

Table of n, a(n) for n=0..32.

Maple

f0:=[1, 1, 3, 11, 6, 14, 12, 4, 14, 4, 12, 14, 5, 11, 9, -11];
f1:=add(f0[i]*x^(i-1), i=1..nops(f0));
f2:=f1/((1-x)^4*(1-x^2)^12);
series(f2, x, 40);
seriestolist(%);

Crossrefs

Sequence in context: A119494 A334544 A268929 * A297632 A153077 A000352

Adjacent sequences: A268241 A268242 A268243 * A268245 A268246 A268247

Keyword

nonn

Author

N. J. A. Sloane, Jan 30 2016

Status

approved