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Number of strings over Z_3 of length n with trace 0 and subtrace 2.
5

%I #24 May 03 2019 02:58:59

%S 0,2,6,12,30,90,252,702,2106,6480,19602,58806,176904,532170,1596510,

%T 4785156,14351094,43053282,129146724,387400806,1162202418,3486725352,

%U 10460294154,31380882462,94143001680,282430067922,847290203766,2541867422652,7625599079310

%N Number of strings over Z_3 of length n with trace 0 and subtrace 2.

%C Same as number of strings over GF(3) of length n with trace 0 and subtrace 2.

%H Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI/GP scripts for miscellaneous math problems</a>

%H F. Ruskey, <a href="http://combos.org/TSstringZ3">Strings over Z_3 with given trace and subtrace</a>

%H F. Ruskey, <a href="http://combos.org/TSstringF3">Strings over GF(3) with given trace and subtrace</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,27,-36,27).

%F a(n; t, s) = a(n-1; t, s) + a(n-1; t+2, s+2t+1) + a(n-1; t+1, s+t+1) where t is the trace and s is the subtrace.

%F G.f.: -2q^2(3*q^3-3*q^2+3*q-1)/[(1-3q)(1+3q^2)(1-3q+3q^2)]. - Lawrence Sze, Oct 24 2004

%Y Cf. A073947, A073948, A073950, A073951, A073952.

%K easy,nonn

%O 1,2

%A _Frank Ruskey_ and Nate Kube, Aug 15 2002

%E Terms a(21) onward from _Max Alekseyev_, Apr 09 2013