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A073947 Number of strings over Z_3 of length n with trace 0 and subtrace 0. 5
1, 1, 3, 9, 21, 63, 225, 729, 2187, 6561, 19845, 59535, 177633, 531441, 1594323, 4782969, 14344533, 43033599, 129127041, 387420489, 1162261467, 3486784401, 10460471301, 31381413903, 94143533121, 282429536481, 847288609443, 2541865828329, 7625594296341 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Same as number of strings over GF(3) of length n with trace 0 and subtrace 0.

LINKS

Table of n, a(n) for n=1..29.

Max Alekseyev, PARI/GP scripts for miscellaneous math problems

F. Ruskey, Strings over Z_3 with given trace and subtrace

F. Ruskey, Strings over GF(3) with given trace and subtrace

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*(21*q^4-21*q^3+12*q^2-5*q+1)/[(1-3q)(1+3q^2)(1-3q+3q^2)]. - Lawrence Sze, Oct 24 2004

EXAMPLE

a(3;0,0)=3 since the three ternary strings of trace 0, subtrace 0 and length 3 are { 000, 111, 222 }.

CROSSREFS

Cf. A073948, A073949, A073950, A073951, A073952.

Sequence in context: A004667 A237122 A326313 * A062811 A236856 A318843

Adjacent sequences:  A073944 A073945 A073946 * A073948 A073949 A073950

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 November 19 00:12 EST 2019. Contains 329310 sequences. (Running on oeis4.)