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A068788
S(n; 1,3) = S(n; 3,3) 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.
10
0, 0, 4, 16, 80, 320, 1120, 4096, 15360, 61440, 254464, 1048576, 4259840, 17039360, 67624960, 268435456, 1069547520, 4278190080, 17146445824, 68719476736, 275146342400, 1100585369600, 4400191897600, 17592186044416, 70351564308480, 281406257233920
OFFSET
1,3
FORMULA
S(n; t, s) = S(n-1; t, s) + S(n-1; t+3, s+3t+1) + S(n-1; t+2, s+2t) + S(n-1; t+1, s+t+1).
Empirical g.f.: 4*x^3*(1-4*x+12*x^2-16*x^3+8*x^4) / ((1-4*x)*(1-4*x+8*x^2)*(1+16*x^4)). - Colin Barker, Feb 21 2016
KEYWORD
nonn,base
AUTHOR
Frank Ruskey, Mar 29 2002
EXTENSIONS
Terms a(11) onward from Max Alekseyev, Apr 09 2013
STATUS
approved