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A073968
Number of strings of length n over Z_5 with trace 1 and subtrace 2.
7
0, 0, 1, 20, 125, 650, 3150, 15625, 78000, 390625, 1952500, 9762500, 48815625, 244125000, 1220703125, 6103593750, 30517656250, 152587890625, 762939062500, 3814697265625, 19073484375000, 95367421875000, 476837119140625, 2384185742187500, 11920928955078125
OFFSET
1,4
COMMENTS
Same as the number of strings of length n over Z_5 with: trace 2 and subtrace 3, trace 3 and subtrace 3, or trace 4 and subtrace 2.
Same as the number of strings of length n over GF(5) with: trace 1 and subtrace 2, trace 2 and subtrace 3, trace 3 and subtrace 3, or trace 4 and subtrace 2.
FORMULA
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).
Empirical g.f.: -x^3*(25*x^4-50*x^3+40*x^2-10*x-1) / ((5*x-1)*(5*x^2-1)*(25*x^4-25*x^3+15*x^2-5*x+1)). - Colin Barker, Nov 26 2014
EXAMPLE
a(3;1,2)=1 since the one 5-ary string of trace 1, subtrace 2 and length 3 is { 222 }.
KEYWORD
easy,nonn
AUTHOR
Frank Ruskey and Nate Kube, Aug 15 2002
EXTENSIONS
Terms a(11) onward from Max Alekseyev, Apr 09 2013
STATUS
approved