A068787 Number of strings over Z_4 of length n with trace 1 and subtrace 2.

0, 2, 6, 16, 56, 192, 896, 4096, 17280, 69632, 270336, 1048576, 4130816, 16515072, 66584576, 268435456, 1077903360, 4311744512, 17213423616, 68719476736, 274609995776, 1098437885952, 4395899027456, 17592186044416, 70385915658240, 281543696187392

Offset

1,2

Comments

a(n; 1,2) = a(n; 3,2) 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.

Same as number of strings over Z_4 of length n with trace 3 and subtrace 2.

Links

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

Max Alekseyev, PARI/GP scripts for miscellaneous math problems

F. Ruskey, Strings over Z_4 with given trace and subtrace

Formula

a(n; t, s) = a(n-1; t, s) + a(n-1; t+3, s+3t+1) + a(n-1; t+2, s+2t) + a(n-1; t+1, s+t+1) where t is the trace and s is the subtrace.

Empirical g.f.: -2*x^2*(16*x^5-16*x^4+4*x^3+8*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, A068777, A068786, A068778, A068788, A068789, A068790.

Sequence in context: A354083 A150029 A221841 * A073959 A006820 A131385

Adjacent sequences: A068784 A068785 A068786 * A068788 A068789 A068790

Keyword

easy,nonn

Author

Frank Ruskey, Nate Kube, Aug 15 2002

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 20 2007

Terms a(11) onward from Max Alekseyev, Apr 14 2013

Status

approved