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A073970
Number of strings of length n over Z_5 with trace 1 and subtrace 4.
7
0, 1, 6, 30, 125, 600, 3025, 15500, 78000, 390625, 1952500, 9765625, 48831250, 244156250, 1220703125, 6103437500, 30517265625, 152587500000, 762939062500, 3814697265625, 19073484375000, 95367431640625, 476837167968750, 2384185839843750, 11920928955078125
OFFSET
1,3
COMMENTS
Same as the number of strings of length n over Z_5 with: trace 2 and subtrace 1, trace 3 and subtrace 1, or trace 4 and subtrace 4.
Same as the number of strings of length n over GF(5) with: trace 1 and subtrace 4, trace 2 and subtrace 1, trace 3 and subtrace 1, or trace 4 and subtrace 4.
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^2*(25*x^5 -50*x^4 +15*x^3 -5*x^2 +4*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
EXAMPLE
a(2;3,2)=2 since the two 5-ary strings of trace 3, subtrace 2 and length 2 are { 12, 21 }.
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