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A068778 S(n; 1,1) = S(n; 3,1) 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, 0, 16, 80, 320, 1184, 4096, 15360, 61440, 253440, 1048576, 4259840, 17039360, 67641344, 268435456, 1069547520, 4278190080, 17146183680, 68719476736, 275146342400, 1100585369600, 4400196091904, 17592186044416, 70351564308480, 281406257233920 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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.: 16*x^3*(1-3*x+4*x^2+2*x^3) / ((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, A068787, A068788, A068789, A068790.

Sequence in context: A212240 A050468 A242167 * A247817 A034570 A165963

Adjacent sequences:  A068775 A068776 A068777 * A068779 A068780 A068781

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 17 20:53 EST 2018. Contains 317278 sequences. (Running on oeis4.)