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A073967
Number of strings of length n over Z_5 with trace 1 and subtrace 1.
7
0, 0, 6, 25, 125, 600, 3150, 15750, 78625, 390625, 1952500, 9762500, 48831250, 244140625, 1220703125, 6103437500, 30517656250, 152588281250, 762941015625, 3814697265625, 19073484375000, 95367421875000, 476837167968750, 2384185791015625, 11920928955078125
OFFSET
1,3
COMMENTS
Same as the number of strings of length n over Z_5 with: trace 2 and subtrace 4, trace 3 and subtrace 4, or trace 4 and subtrace 1.
Same as the number of strings of length n over GF(5) with: trace 1 and subtrace 1, trace 2 and subtrace 4, trace 3 and subtrace 4, or trace 4 and subtrace 1.
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+75*x^3-85*x^2+35*x-6) / ((5*x-1)*(5*x^2-1)*(25*x^4-25*x^3+15*x^2-5*x+1)). - Colin Barker, Nov 26 2014
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