A068774 Number of strings over Z_4 of length n with trace 0 and subtrace 2.

0, 0, 0, 8, 40, 240, 1120, 4480, 17280, 65280, 253440, 1015808, 4126720, 16773120, 67624960, 270499840, 1077903360, 4294901760, 17146183680, 68585259008, 274608947200, 1099510579200, 4400191897600, 17600767590400, 70385915658240, 281474959933440

Offset

1,4

Comments

a(n; 0,2) where a(n; t,s) is the number of length n 4-ary strings whose digits sum to t mod 4 and whose sum of products of all pairs of digits sum to s mod 4.

Links

Table of n, a(n) for n=1..26.

Max Alekseyev, PARI/GP scripts for miscellaneous math problems

F. Ruskey, Strings over Z_4 with given trace and subtrace

Formula

a(n; t, s) = a(n-1; t, s) + a(n-1; t+3, s+3t+1) + a(n-1; t+2, s+2t) + a(n-1; t+1, s+t+1) where t is the trace and s is the subtrace.

Empirical g.f.: 8*x^4*(40*x^4-40*x^3+20*x^2-5*x+1) / ((2*x-1)*(4*x-1)*(8*x^2-4*x+1)*(16*x^4+1)). - Colin Barker, Dec 06 2014

Crossrefs

Cf. A068620, A068711, A068777, A068786, A068778, A068787, A068788, A068789, A068790.

Sequence in context: A228679 A188234 A068775 * A073955 A264332 A188332

Adjacent sequences: A068771 A068772 A068773 * A068775 A068776 A068777

Keyword

easy,nonn

Author

Frank Ruskey and Nate Kube, Aug 15 2002

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 20 2007

Terms a(11) onward from Max Alekseyev, Apr 09 2013

Status

approved