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

1,2

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

Table of n, a(n) for n=1..29.

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).

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

Mathematica

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

Crossrefs

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

Sequence in context: A176678 A277251 A275165 * A281270 A322752 A277345

Adjacent sequences: A073947 A073948 A073949 * A073951 A073952 A073953

Keyword

easy,nonn

Author

Frank Ruskey and Nate Kube, Aug 15 2002

Extensions

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

Status

approved