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.
LINKS
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 }.
CROSSREFS
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