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T(n,k)=Number of 0..2 arrays of length n+2*k-1 with sum less than 2*k in any length 2k subsequence (=less than 50% duty cycle)
14

%I #4 May 25 2012 20:46:12

%S 3,31,5,294,67,8,2727,690,148,13,25048,6681,1669,322,21,228826,63052,

%T 16878,4057,677,34,2083371,587036,163495,43050,9807,1439,55,18925047,

%U 5420945,1549297,428617,109995,23401,3086,89,171633840,49790907,14492156

%N T(n,k)=Number of 0..2 arrays of length n+2*k-1 with sum less than 2*k in any length 2k subsequence (=less than 50% duty cycle)

%C Table starts

%C ..3...31....294....2727....25048....228826....2083371....18925047....171633840

%C ..5...67....690....6681....63052....587036....5420945....49790907....455613780

%C ..8..148...1669...16878...163495...1549297...14492156...134429604...1239807015

%C .13..322...4057...43050...428617...4135249...39179582...366956550...3410099667

%C .21..677...9807..109995..1128418..11095332..106521624..1007510947...9434164257

%C .34.1439..23401..280255..2972836..29835132..290452176..2775231053..26189744683

%C .55.3086..54747..709626..7819020..80249504..792966548..7657995382..72853584571

%C .89.6625.128892.1780062.20492970.215618862.2165136076.21147760860.202893735787

%H R. H. Hardin, <a href="/A212729/b212729.txt">Table of n, a(n) for n = 1..1121</a>

%e Some solutions for n=3 k=4

%e ..2....1....1....0....1....2....1....0....0....1....2....2....1....0....2....2

%e ..2....0....1....0....1....0....0....1....0....1....1....0....1....2....0....0

%e ..0....1....1....1....0....1....1....1....0....0....0....0....2....2....1....1

%e ..0....0....1....1....2....0....1....1....1....1....0....1....1....1....0....0

%e ..0....0....2....0....0....2....1....1....0....1....0....1....0....0....2....2

%e ..0....1....0....0....1....1....1....0....2....1....0....0....0....1....1....0

%e ..0....0....1....2....1....1....0....0....2....0....1....0....0....0....0....0

%e ..2....0....0....1....1....0....0....2....1....0....1....0....0....0....1....1

%e ..2....1....0....0....0....0....1....0....1....2....1....0....1....0....0....1

%e ..2....0....2....0....2....2....1....1....0....2....1....1....0....2....2....0

%Y Column 1 is A000045(n+3)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ May 25 2012