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A073950
Number of strings over Z_3 of length n with trace 1 and subtrace 0.
6
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
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]
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
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