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%I #23 May 03 2019 02:59:13
%S 1,1,1,25,125,625,3025,15625,78625,393125,1955625,9765625,48815625,
%T 244140625,1220703125,6103515625,30517265625,152587890625,
%U 762941015625,3814705078125,19073494140625,95367431640625,476837119140625,2384185791015625,11920928955078125
%N Number of strings of length n over Z_5 with trace 0 and subtrace 0.
%C Same as the number of strings of length n over GF(5) with trace 0 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*(525*x^6-525*x^5+190*x^4-26*x^2+9*x-1) / ((5*x-1)*(5*x^2-1)*(25*x^4-25*x^3+15*x^2-5*x+1)). - _Colin Barker_, Apr 03 2015
%Y Cf. A073964, A073965, A073966, A073967, A073968, A073969, A073970.
%K easy,nonn
%O 1,4
%A _Frank Ruskey_ and Nate Kube, Aug 15 2002
%E Terms a(11) onward from _Max Alekseyev_, Apr 09 2013
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