duplicate hunting
Maximilian Hasler
maximilian.hasler at gmail.com
Sat May 19 16:00:35 CEST 2007
I don't remember if these have already been listed.
Given terms and formula are identical.
Maximilian
http://www.research.att.com/~njas/sequences/?q=1%2C2%2C4%2C8%2C56%2C272
A073953 Number of strings over Z_4 of length n with trace 0 and
subtrace 0.
1, 2, 4, 8, 56, 272, 1184, 4763, 17536, 65792 (list; graph; listen)
LINKS F. Ruskey, Strings over Z_4 of 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.
EXAMPLE
a(3;0,0)=4 since the four 4-ary strings of trace 0, subtrace 0 and
length 3 are { 000, 022, 202, 220 }.
CROSSREFS
Cf. A068711, A073955, A068777, A068786, A068778, A073959, A068788,
A068789, A073962.
AUTHOR Frank Ruskey, Nate Kube (fruskey(AT)cs.uvic.ca), Aug 15 2002
A068620 S(n; 0,0) 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, 4, 8, 56, 272, 1184, 4736, 17536, 65792 (list; graph; listen)
LINKS 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)
EXAMPLE S(3;0,0) = 4 = |{000,022,202,220}|.
AUTHOR Frank Ruskey (fruskey(AT)cs.uvic.ca), Mar 29 2002
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