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T(n,k)=Number of 0..2 arrays of length n+2*k-1 with sum no more than 2*k in any length 2k subsequence (=50% duty cycle)
14

%I #4 May 06 2012 19:33:30

%S 6,50,14,435,124,31,3834,1113,311,70,34001,10002,2902,775,157,302615,

%T 89911,26637,7596,1895,353,2699598,808403,242780,71427,19834,4663,793,

%U 24121674,7269626,2204646,660796,191853,51440,11518,1782,215786649

%N T(n,k)=Number of 0..2 arrays of length n+2*k-1 with sum no more than 2*k in any length 2k subsequence (=50% duty cycle)

%C Table starts

%C ....6....50....435....3834....34001....302615....2699598....24121674

%C ...14...124...1113...10002....89911....808403....7269626....65380788

%C ...31...311...2902...26637...242780...2204646...19976155...180744711

%C ...70...775...7596...71427...660796...6062948...55360211...503916387

%C ..157..1895..19834..191853..1804448..16740414..154089343..1411275807

%C ..353..4663..51440..514687..4931630..46305966..429886243..3962696059

%C ..793.11518.131950.1376128.13468524.128148456.1200645159.11143104246

%C .1782.28446.339564.3659968.36711516.354470546.3354267511.31356940932

%H R. H. Hardin, <a href="/A212232/b212232.txt">Table of n, a(n) for n = 1..1074</a>

%e Some solutions for n=3 k=4

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

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

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

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

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

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

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

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

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

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

%Y Column 1 is A006356(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ May 06 2012