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%I #22 May 03 2019 07:17:38
%S 0,2,6,30,125,650,3150,15750,78000,390625,1952500,9768750,48831250,
%T 244156250,1220703125,6103593750,30517656250,152588281250,
%U 762939062500,3814697265625,19073484375000,95367441406250,476837167968750,2384185839843750,11920928955078125
%N Number of strings of length n over Z_5 with trace 1 and subtrace 3.
%C Same as the number of strings of length n over Z_5 with: trace 2 and subtrace 2, trace 3 and subtrace 2, or trace 4 and subtrace 3.
%C Same as the number of strings of length n over GF(5) with: trace 1 and subtrace 3, trace 2 and subtrace 2, trace 3 and subtrace 2, or trace 4 and subtrace 3.
%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^2*(25*x^5-50*x^4+65*x^3-40*x^2+14*x-2) / ((5*x-1)*(5*x^2-1)*(25*x^4-25*x^3+15*x^2-5*x+1)). - _Colin Barker_, Nov 26 2014
%e a(2;3,2)=2 since the two 5-ary strings of trace 3, subtrace 2 and length 2 are { 12, 21 }.
%Y Cf. A073963, A073964, A073965, A073966, A073967, A073968, A073970.
%K easy,nonn
%O 1,2
%A _Frank Ruskey_ and Nate Kube, Aug 15 2002
%E Terms a(11) onward from _Max Alekseyev_, Apr 09 2013
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