A068786 S(n; 1,0) = S(n; 3,0) 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.

1, 2, 6, 16, 40, 192, 896, 4096, 17536, 69632, 270336, 1048576, 4126720, 16515072, 66584576, 268435456, 1077968896, 4311744512, 17213423616, 68719476736, 274608947200, 1098437885952, 4395899027456, 17592186044416, 70385932435456, 281543696187392

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.: x*(1-6*x+14*x^2-16*x^3+8*x^4-32*x^5+32*x^6) / ((1-4*x)*(1-4*x+8*x^2)*(1+16*x^4)). - Colin Barker, Feb 21 2016

Crossrefs

Cf. A068620, A068711, A068774, A068777, A068778, A068787, A068788, A068789, A068790.

Sequence in context: A018021 A215340 A074405 * A276359 A158920 A263592

Adjacent sequences: A068783 A068784 A068785 * A068787 A068788 A068789

Keyword

nonn,base

Author

Frank Ruskey, Mar 29 2002

Extensions

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

Status

approved