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A212232 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).

%I A212232 #6 Jun 02 2025 07:55:57
%S A212232 6,50,14,435,124,31,3834,1113,311,70,34001,10002,2902,775,157,302615,
%T A212232 89911,26637,7596,1895,353,2699598,808403,242780,71427,19834,4663,793,
%U A212232 24121674,7269626,2204646,660796,191853,51440,11518,1782,215786649
%N A212232 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 A212232 Table starts
%C A212232 ....6....50....435....3834....34001....302615....2699598....24121674
%C A212232 ...14...124...1113...10002....89911....808403....7269626....65380788
%C A212232 ...31...311...2902...26637...242780...2204646...19976155...180744711
%C A212232 ...70...775...7596...71427...660796...6062948...55360211...503916387
%C A212232 ..157..1895..19834..191853..1804448..16740414..154089343..1411275807
%C A212232 ..353..4663..51440..514687..4931630..46305966..429886243..3962696059
%C A212232 ..793.11518.131950.1376128.13468524.128148456.1200645159.11143104246
%C A212232 .1782.28446.339564.3659968.36711516.354470546.3354267511.31356940932
%H A212232 R. H. Hardin, <a href="/A212232/b212232.txt">Table of n, a(n) for n = 1..1074</a>
%e A212232 Some solutions for n=3 k=4
%e A212232 ..1....2....2....1....2....0....1....2....2....1....1....2....0....0....1....1
%e A212232 ..1....0....0....1....1....1....0....2....2....0....0....2....0....1....1....1
%e A212232 ..1....2....2....0....0....0....0....1....0....1....0....0....1....0....0....2
%e A212232 ..0....0....1....1....1....2....2....1....1....1....0....0....1....0....1....1
%e A212232 ..0....1....0....0....1....2....0....1....1....1....0....1....0....1....1....2
%e A212232 ..0....0....2....1....1....0....1....1....1....1....1....2....1....0....0....0
%e A212232 ..1....1....0....1....1....0....0....0....0....2....2....1....0....2....1....0
%e A212232 ..1....1....0....1....0....0....0....0....0....0....2....0....1....1....1....0
%e A212232 ..1....1....1....1....1....1....0....1....1....1....2....0....0....1....0....0
%e A212232 ..0....1....2....2....2....0....0....2....1....1....1....1....2....1....0....1
%Y A212232 Column 1 is A006356(n+1)
%K A212232 nonn,tabl
%O A212232 1,1
%A A212232 _R. H. Hardin_ May 06 2012