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A049294 Number of subgroups of index 3 in free group of rank n+1. 5


%S 1,13,97,625,3841,23233,139777,839425,5038081,30231553,181395457,

%T 1088385025,6530334721,39182057473,235092443137,1410554855425,

%U 8463329525761,50779977940993,304679869218817,1828079218458625

%N Number of subgroups of index 3 in free group of rank n+1.

%D P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 23.

%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(b).

%H Harvey P. Dale, <a href="/A049294/b049294.txt">Table of n, a(n) for n = 0..1000</a>

%H M. Hall, <a href="http://dx.doi.org/10.4153/CJM-1949-017-2">Subgroups of finite index in free groups</a>, Canad. J. Math., 1 (1949), 187-190.

%H V. A. Liskovets and A. Mednykh, <a href="http://dx.doi.org/10.1080/00927870008826924">Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces</a>, Commun. in Algebra, 28, No. 4 (2000), 1717-1738.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-20,12).

%F a(n) = 3*6^n-3*2^n+1.

%F G.f.: (1+4*x)/((1-x)*(1-2*x)*(1-6*x)). [_Colin Barker_, May 08 2012]

%t LinearRecurrence[{9,-20,12},{1,13,97},20] (* _Harvey P. Dale_, Sep 24 2017 *)

%Y Cf. A003319, A027837, A049290, A049291, A049292, A049293, A049295.

%K easy,nice,nonn

%O 0,2

%A _Valery A. Liskovets_

%E More terms from Karen Richardson (s1149414(AT)cedarville.edu)

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Last modified January 17 14:57 EST 2020. Contains 330958 sequences. (Running on oeis4.)