A073947 Number of strings over Z_3 of length n with trace 0 and subtrace 0.

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

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 A363693 A236856

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