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%I #30 Apr 30 2019 11:23:57
%S 0,0,4,16,80,320,1120,4096,15360,61440,254464,1048576,4259840,
%T 17039360,67624960,268435456,1069547520,4278190080,17146445824,
%U 68719476736,275146342400,1100585369600,4400191897600,17592186044416,70351564308480,281406257233920
%N S(n; 1,3) = S(n; 3,3) 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.: 4*x^3*(1-4*x+12*x^2-16*x^3+8*x^4) / ((1-4*x)*(1-4*x+8*x^2)*(1+16*x^4)). - _Colin Barker_, Feb 21 2016
%Y Cf. A068620, A068711, A068774, A068777, A068786, A068778, A068787, A068789, A068790.
%K nonn,base
%O 1,3
%A _Frank Ruskey_, Mar 29 2002
%E Terms a(11) onward from _Max Alekseyev_, Apr 09 2013
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