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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 (list; graph; refs; listen; history; text; internal format)
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 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

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Last modified September 22 15:04 EDT 2021. Contains 347607 sequences. (Running on oeis4.)