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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).
0
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.
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 30 2016
STATUS
approved