A068777 S(n; 0,3) = S(n; 2,1) 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, 2, 6, 24, 80, 240, 896, 3584, 15360, 65792, 270336, 1081344, 4259840, 16773120, 66584576, 266338304, 1069547520, 4295032832, 17213423616, 68853694464, 275146342400, 1099510579200, 4395899027456, 17583596109824, 70351564308480, 281474993487872

Offset

1,2

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.: 2*x^2*(16*x^5-8*x^4+16*x^3-12*x^2+5*x-1) / ((4*x-1)*(8*x^2-4*x+1)*(16*x^4+1)). - Colin Barker, Dec 06 2014

Crossrefs

Cf. A068620, A068711, A068774, A068786, A068778, A068787, A068788, A068789, A068790.

Sequence in context: A002526 A324373 A117665 * A372854 A275206 A095110

Adjacent sequences: A068774 A068775 A068776 * A068778 A068779 A068780

Keyword

nonn,base

Author

Frank Ruskey, Mar 29 2002

Extensions

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

Status

approved