%I #23 Oct 10 2024 12:09:40

%S 0,0,3,12,30,81,252,756,2187,6480,19602,59049,176904,530712,1594323,

%T 4785156,14351094,43046721,129146724,387440172,1162261467,3486725352,

%U 10460294154,31381059609,94143001680,282429005040,847288609443,2541867422652,7625599079310

%N Number of strings over Z_3 of length n with trace 1 and subtrace 2.

%C Same as number of strings over Z_3 of length n with trace 2 and subtrace 2. Same as number of strings over GF(3) of length n with trace 1 and subtrace 2. Same as number of strings over GF(3) of length n with trace 2 and subtrace 2.

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

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

%H Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI/GP scripts for miscellaneous math problems</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.: 3q^3(q^2-2*q+1)/[(1-3q)(1+3q^2)(1-3q+3q^2)]. - Lawrence Sze, Oct 24 2004

%e a(3;1,2)=3 since the three ternary strings of trace 1, subtrace 2 and length 3 are { 112, 121, 211 }.

%t LinearRecurrence[{6,-15,27,-36,27},{0,0,3,12,30},30] (* _Harvey P. Dale_, Oct 22 2019 *)

%Y Cf. A073947, A073948, A073949, A073950, A073951.

%K easy,nonn,changed

%O 1,3

%A _Frank Ruskey_ and Nate Kube, Aug 15 2002

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