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.

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

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