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A068787
Number of strings over Z_4 of length n with trace 1 and subtrace 2.
10
0, 2, 6, 16, 56, 192, 896, 4096, 17280, 69632, 270336, 1048576, 4130816, 16515072, 66584576, 268435456, 1077903360, 4311744512, 17213423616, 68719476736, 274609995776, 1098437885952, 4395899027456, 17592186044416, 70385915658240, 281543696187392
OFFSET
1,2
COMMENTS
a(n; 1,2) = a(n; 3,2) where S(n; t,s) is the number of length n 4-ary strings whose digits sum to t mod 4 and whose sum of products of all pairs of digits sum to s mod 4.
Same as number of strings over Z_4 of length n with trace 3 and subtrace 2.
FORMULA
a(n; t, s) = a(n-1; t, s) + a(n-1; t+3, s+3t+1) + a(n-1; t+2, s+2t) + a(n-1; t+1, s+t+1) where t is the trace and s is the subtrace.
Empirical g.f.: -2*x^2*(16*x^5-16*x^4+4*x^3+8*x^2-5*x+1) / ((4*x-1)*(8*x^2-4*x+1)*(16*x^4+1)). - Colin Barker, Dec 06 2014
KEYWORD
easy,nonn
AUTHOR
Frank Ruskey, Nate Kube, Aug 15 2002
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 20 2007
Terms a(11) onward from Max Alekseyev, Apr 14 2013
STATUS
approved