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%I #32 Apr 30 2019 11:24:02
%S 1,2,4,16,56,272,1184,4608,17536,65792,254464,1017856,4130816,
%T 16781312,67641344,270532608,1077968896,4295032832,17146445824,
%U 68585783296,274609995776,1099512676352,4400196091904,17600775979008,70385932435456,281474993487872
%N S(n; 2,0) 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*(1-8*x+24*x^2-24*x^3-24*x^4+32*x^5+64*x^6-192*x^7) / ((1-2*x)*(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, A068788, 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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