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%I #30 Apr 30 2019 11:23:51
%S 1,2,6,16,40,192,896,4096,17536,69632,270336,1048576,4126720,16515072,
%T 66584576,268435456,1077968896,4311744512,17213423616,68719476736,
%U 274608947200,1098437885952,4395899027456,17592186044416,70385932435456,281543696187392
%N S(n; 1,0) = S(n; 3,0) 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.: x*(1-6*x+14*x^2-16*x^3+8*x^4-32*x^5+32*x^6) / ((1-4*x)*(1-4*x+8*x^2)*(1+16*x^4)). - _Colin Barker_, Feb 21 2016
%Y Cf. A068620, A068711, A068774, A068777, 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
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