A068777 - OEIS

%I #27 Apr 30 2019 11:23:05

%S 0,2,6,24,80,240,896,3584,15360,65792,270336,1081344,4259840,16773120,

%T 66584576,266338304,1069547520,4295032832,17213423616,68853694464,

%U 275146342400,1099510579200,4395899027456,17583596109824,70351564308480,281474993487872

%N S(n; 0,3) = S(n; 2,1) where S(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://combos.org/TSstringS4">4-ary strings with given trace and subtrace</a>

%F S(n; t, s) = S(n-1; t, s) + S(n-1; t+3, s+3t+1) + S(n-1; t+2, s+2t) + S(n-1; t+1, s+t+1).

%F Empirical g.f.: 2*x^2*(16*x^5-8*x^4+16*x^3-12*x^2+5*x-1) / ((4*x-1)*(8*x^2-4*x+1)*(16*x^4+1)). - _Colin Barker_, Dec 06 2014

%Y Cf. A068620, A068711, A068774, A068786, A068778, A068787, A068788, A068789, A068790.

%K nonn,base

%O 1,2

%A _Frank Ruskey_, Mar 29 2002

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