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

1, 2, 3, 9, 30, 81, 225, 702, 2187, 6561, 19602, 59049, 177633, 532170, 1594323, 4782969, 14351094, 43046721, 129127041, 387400806, 1162261467, 3486784401, 10460294154, 31381059609, 94143533121, 282430067922, 847288609443, 2541865828329, 7625599079310

Offset: 1

Author

Frank Ruskey and Nate Kube, Aug 15 2002

Keywords

• easy
• nonn

Comments

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.

Links

• Max Alekseyev, PARI/GP scripts for miscellaneous math problems
• Katarzyna Grygiel, Pawel M. Idziak and Marek Zaionc, How big is BCI fragment of BCK logic, arXiv preprint arXiv:1112.0643 [cs.LO], 2011. [_N. J. A. Sloane_, Feb 21 2012]
• F. Ruskey, Strings over Z_3 with given trace and subtrace
• F. Ruskey, Strings over GF(3) with given trace and subtrace
• Index entries for linear recurrences with constant coefficients, signature (6,-15,27,-36,27).

Crossrefs

Cf. A073947, A073948, A073949, A073951, A073952.

Programs

Mathematica

LinearRecurrence[{6, -15, 27, -36, 27}, {1, 2, 3, 9, 30}, 30] (* Jean-François Alcover, Jan 07 2019 *)

Formula

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.

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

Extensions

Terms a(21) onward from Max Alekseyev, Apr 09 2013