

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
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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(n1; t, s) + a(n1; t+2, s+2t+1) + a(n1; t+1, s+t+1) where t is the trace and s is the subtrace.
G.f.: 3q^3(q^22*q+1)/[(13q)(1+3q^2)(13q+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 A293656 A131936
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



