A073952 Number of strings over Z_3 of length n with trace 1 and subtrace 2.

0, 0, 3, 12, 30, 81, 252, 756, 2187, 6480, 19602, 59049, 176904, 530712, 1594323, 4785156, 14351094, 43046721, 129146724, 387440172, 1162261467, 3486725352, 10460294154, 31381059609, 94143001680, 282429005040, 847288609443, 2541867422652, 7625599079310

Offset

1,3

Comments

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.

Links

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

F. Ruskey, Strings over Z_3 with given trace and subtrace

F. Ruskey, Strings over GF(3) with given trace and subtrace

Max Alekseyev, PARI/GP scripts for miscellaneous math problems

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

Example

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

Mathematica

LinearRecurrence[{6, -15, 27, -36, 27}, {0, 0, 3, 12, 30}, 30] (* Harvey P. Dale, Oct 22 2019 *)

Crossrefs

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

Sequence in context: A281434 A296289 A089143 * A107231 A363913 A352157

Adjacent sequences: A073949 A073950 A073951 * A073953 A073954 A073955

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