cp's OEIS Frontend

A073950 Number of strings over Z_3 of length n with trace 1 and subtrace 0.

%I A073950 #30 May 03 2019 03:04:27
%S A073950 1,2,3,9,30,81,225,702,2187,6561,19602,59049,177633,532170,1594323,
%T A073950 4782969,14351094,43046721,129127041,387400806,1162261467,3486784401,
%U A073950 10460294154,31381059609,94143533121,282430067922,847288609443,2541865828329,7625599079310
%N A073950 Number of strings over Z_3 of length n with trace 1 and subtrace 0.
%C A073950 Same as number of strings over Z_3 of length n with trace 2 and subtrace 0. Same as number of strings over GF(3) of length n with trace 1 and subtrace 0. Same as number of strings over GF(3) of length n with trace 2 and subtrace 0.
%H A073950 Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI/GP scripts for miscellaneous math problems</a>
%H A073950 Katarzyna Grygiel, Pawel M. Idziak and Marek Zaionc, <a href="http://arxiv.org/abs/1112.0643">How big is BCI fragment of BCK logic</a>, arXiv preprint arXiv:1112.0643 [cs.LO], 2011. [_N. J. A. Sloane_, Feb 21 2012]
%H A073950 F. Ruskey, <a href="http://combos.org/TSstringZ3">Strings over Z_3 with given trace and subtrace</a>
%H A073950 F. Ruskey, <a href="http://combos.org/TSstringF3">Strings over GF(3) with given trace and subtrace</a>
%H A073950 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,27,-36,27).
%F A073950 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 A073950 G.f.: q*(q-1)*(3*q^3-3*q^2+3*q-1)/[(1-3q)(1+3q^2)(1-3q+3q^2)]. - Lawrence Sze, Oct 24 2004
%t A073950 LinearRecurrence[{6, -15, 27, -36, 27}, {1, 2, 3, 9, 30}, 30] (* _Jean-François Alcover_, Jan 07 2019 *)
%Y A073950 Cf. A073947, A073948, A073949, A073951, A073952.
%K A073950 easy,nonn
%O A073950 1,2
%A A073950 _Frank Ruskey_ and Nate Kube, Aug 15 2002
%E A073950 Terms a(21) onward from _Max Alekseyev_, Apr 09 2013