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A073952
Number of strings over Z_3 of length n with trace 1 and subtrace 2.
5
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.
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 ternary 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
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