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%I #26 May 03 2019 07:17:27
%S 1,2,6,20,125,625,3150,15500,78000,390625,1955625,9768750,48831250,
%T 244125000,1220703125,6103515625,30517656250,152587500000,
%U 762939062500,3814697265625,19073494140625,95367441406250,476837167968750,2384185742187500,11920928955078125
%N Number of strings of length n over Z_5 with trace 1 and subtrace 0.
%C Same as the number of strings of length n over Z_5 with: trace 2 and subtrace 0, trace 3 and subtrace 0, or trace 4 and subtrace 0.
%C Same as the number of strings of length n over GF(5) with: trace 2 and subtrace 0, or trace 3 and subtrace 0.
%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/TSstringZ5">Strings over Z_5 with given trace and subtrace</a>
%H F. Ruskey, <a href="http://combos.org/TSstringF5">Strings over GF(5) with given trace and subtrace</a>
%F a(n; t, s) = a(n-1; t, s) + a(n-1; t+4, s+4t+1) + a(n-1; t+3, s+3t+4) + a(n-1; t+2, s+2t+4) + a(n-1; t+1, s+t+1).
%F Empirical g.f.: -x*(25*x^6 -50*x^5 +15*x^4 +20*x^3 -21*x^2 +8*x -1) / ((5*x -1)*(5*x^2 -1)*(25*x^4 -25*x^3 +15*x^2 -5*x +1)). - _Colin Barker_, Nov 25 2014
%Y Cf. A073963, A073964, A073965, A073967, A073968, A073969, A073970.
%K easy,nonn
%O 1,2
%A _Frank Ruskey_, Nate Kube, Aug 15 2002
%E Terms a(11) onward from _Max Alekseyev_, Apr 09 2013