A073949 Number of strings over Z_3 of length n with trace 0 and subtrace 2.

0, 2, 6, 12, 30, 90, 252, 702, 2106, 6480, 19602, 58806, 176904, 532170, 1596510, 4785156, 14351094, 43053282, 129146724, 387400806, 1162202418, 3486725352, 10460294154, 31380882462, 94143001680, 282430067922, 847290203766, 2541867422652, 7625599079310

Offset

1,2

Comments

Same as number of strings over GF(3) of length n with trace 0 and subtrace 2.

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

Crossrefs

Cf. A073947, A073948, A073950, A073951, A073952.

Sequence in context: A291445 A320664 A022916 * A367336 A080372 A335287

Adjacent sequences: A073946 A073947 A073948 * A073950 A073951 A073952

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