A073951 Number of strings over Z_3 of length n with trace 1 and subtrace 1.

0, 1, 3, 6, 21, 81, 252, 729, 2187, 6642, 19845, 59049, 176904, 531441, 1594323, 4780782, 14344533, 43046721, 129146724, 387420489, 1162261467, 3486843450, 10460471301, 31381059609, 94143001680, 282429536481, 847288609443, 2541864234006, 7625594296341

Offset: 1

Author

Frank Ruskey and Nate Kube, Aug 15 2002

Keywords

• easy
• nonn

Comments

Same as number of strings over Z_3 of length n with trace 2 and subtrace 1. Same as number of strings over GF(3) of length n with trace 1 and subtrace 1. Same as number of strings over GF(3) of length n with trace 2 and subtrace 1.

Examples

			a(2;2,1)=1 since the one ternary string of trace 2, subtrace 1 and length 2 is { 11 }.
		

Links

• 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).

Crossrefs

Cf. A073947, A073948, A073949, A073950, A073952.

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

Extensions

Terms a(21) onward from Max Alekseyev, Apr 09 2013