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A068774 Number of strings over Z_4 of length n with trace 0 and subtrace 2. 11


%S 0,0,0,8,40,240,1120,4480,17280,65280,253440,1015808,4126720,16773120,

%T 67624960,270499840,1077903360,4294901760,17146183680,68585259008,

%U 274608947200,1099510579200,4400191897600,17600767590400,70385915658240,281474959933440

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

%C 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.

%H Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI/GP scripts for miscellaneous math problems</a>

%H F. Ruskey, <a href="http://www.theory.csc.uvic.ca/~cos/inf/trs/str/Zq/str_tr_subtr_Z4.html">Strings over Z_4 of given Trace and Subtrace</a>

%F 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.

%F 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

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

%K easy,nonn

%O 1,4

%A _Frank Ruskey_ and Nate Kube, Aug 15 2002

%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 20 2007

%E Terms a(11) onward from _Max Alekseyev_, Apr 09 2013

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Last modified November 14 19:12 EST 2018. Contains 317214 sequences. (Running on oeis4.)