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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. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..26.

Max Alekseyev, PARI/GP scripts for miscellaneous math problems

F. Ruskey, 4-ary strings with given trace and subtrace.

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

CROSSREFS

Cf. A068620, A068711, A068774, A068777, A068786, A068778, A068787, A068789, A068790.

Sequence in context: A221763 A009318 A081682 * A094013 A106568 A183146

Adjacent sequences:  A068785 A068786 A068787 * A068789 A068790 A068791

KEYWORD

nonn,base

AUTHOR

Frank Ruskey, Mar 29 2002

EXTENSIONS

Terms a(11) onward from Max Alekseyev, Apr 09 2013

STATUS

approved

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Last modified November 16 12:40 EST 2018. Contains 317272 sequences. (Running on oeis4.)