A073951 Number of strings over Z_3 of length n with trace 1 and subtrace 1.

0, 1, 3, 6, 21, 81, 252, 729, 2187, 6642, 19845, 59049, 176904, 531441, 1594323, 4780782, 14344533, 43046721, 129146724, 387420489, 1162261467, 3486843450, 10460471301, 31381059609, 94143001680, 282429536481, 847288609443, 2541864234006, 7625594296341

Offset

1,3

Comments

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

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

Example

a(2;2,1)=1 since the one ternary string of trace 2, subtrace 1 and length 2 is { 11 }.

Crossrefs

Cf. A073947, A073948, A073949, A073950, A073952.

Sequence in context: A218244 A151961 A025229 * A032098 A292066 A019053

Adjacent sequences: A073948 A073949 A073950 * A073952 A073953 A073954

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