OFFSET
1,2
COMMENTS
a(n; 0,0) where a(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.
LINKS
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.: -x*(704*x^7-704*x^6+288*x^5-56*x^4+32*x^3-24*x^2+8*x-1) / ((2*x-1)*(4*x-1)*(8*x^2-4*x+1)*(16*x^4+1)). - Colin Barker, Dec 06 2014
EXAMPLE
a(3;0,0)=4 since the four 4-ary strings of trace 0, subtrace 0 and length 3 are { 000, 022, 202, 220 }.
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Frank Ruskey and Nate Kube, Aug 15 2002
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 19 2007
Terms a(11) onward from Max Alekseyev, Apr 14 2013
STATUS
approved