

A068774


Number of strings over Z_4 of length n with trace 0 and subtrace 2.


11



0, 0, 0, 8, 40, 240, 1120, 4480, 17280, 65280, 253440, 1015808, 4126720, 16773120, 67624960, 270499840, 1077903360, 4294901760, 17146183680, 68585259008, 274608947200, 1099510579200, 4400191897600, 17600767590400, 70385915658240, 281474959933440
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OFFSET

1,4


COMMENTS

a(n; 0,2) where a(n; t,s) is the number of length n 4ary strings whose digits sum to t mod 4 and whose sum of products of all pairs of digits sum to s mod 4.


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(n1; t, s) + a(n1; t+3, s+3t+1) + a(n1; t+2, s+2t) + a(n1; t+1, s+t+1) where t is the trace and s is the subtrace.
Empirical g.f.: 8*x^4*(40*x^440*x^3+20*x^25*x+1) / ((2*x1)*(4*x1)*(8*x^24*x+1)*(16*x^4+1)).  Colin Barker, Dec 06 2014


CROSSREFS

Cf. A068620, A068711, A068777, A068786, A068778, A068787, A068788, A068789, A068790.
Sequence in context: A228679 A188234 A068775 * A073955 A264332 A188332
Adjacent sequences: A068771 A068772 A068773 * A068775 A068776 A068777


KEYWORD

easy,nonn


AUTHOR

Frank Ruskey and 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 09 2013


STATUS

approved



