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A213464 T(n,k)=Number of 0..3 arrays of length n+2*k-1 with sum less than 3*k in any length 2k subsequence (=less than 50% duty cycle).

%I A213464 #6 Jun 02 2025 08:01:47
%S A213464 6,106,14,1758,310,31,28722,5542,927,70,466136,94238,18018,2735,157,
%T A213464 7536790,1568984,319078,58898,7803,353,121573668,25829770,5444644,
%U A213464 1091036,191573,22506,793,1957953138,422335348,91147915,19105020,3737885
%N A213464 T(n,k)=Number of 0..3 arrays of length n+2*k-1 with sum less than 3*k in any length 2k subsequence (=less than 50% duty cycle).
%C A213464 Table starts
%C A213464 ....6....106....1758.....28722.....466136.....7536790....121573668
%C A213464 ...14....310....5542.....94238....1568984....25829770....422335348
%C A213464 ...31....927...18018....319078....5444644....91147915...1508740928
%C A213464 ...70...2735...58898...1091036...19105020...325333429...5451265872
%C A213464 ..157...7803..191573...3737885...67329406..1167362677..19808276303
%C A213464 ..353..22506..615561..12773955..237475982..4198162231..72188618371
%C A213464 ..793..65425.1940673..43399990..836356119.15103463125.263422708979
%C A213464 .1782.190318.6155514.146145812.2935825527.54284048195.961420842175
%H A213464 R. H. Hardin, <a href="/A213464/b213464.txt">Table of n, a(n) for n = 1..897</a>
%e A213464 Some solutions for n=3 k=4
%e A213464 ..2....0....2....0....0....0....2....0....0....2....0....0....0....2....0....0
%e A213464 ..2....2....0....2....1....2....2....0....0....0....0....1....1....2....2....0
%e A213464 ..2....1....0....0....0....3....0....0....0....0....0....2....0....1....1....0
%e A213464 ..1....3....1....1....0....0....0....2....0....0....2....0....0....1....1....1
%e A213464 ..1....1....1....3....2....0....2....2....0....3....3....0....0....1....0....2
%e A213464 ..0....1....3....1....2....2....1....2....0....0....0....0....0....2....2....0
%e A213464 ..1....0....0....0....1....0....1....0....0....0....1....0....2....1....1....1
%e A213464 ..1....1....0....0....1....0....3....0....0....2....0....2....2....0....2....2
%e A213464 ..2....0....2....1....3....0....2....1....2....2....1....0....2....2....2....2
%e A213464 ..3....3....0....3....0....2....1....3....2....3....2....0....2....1....1....2
%Y A213464 Column 1 is A006356(n+1)
%K A213464 nonn,tabl
%O A213464 1,1
%A A213464 _R. H. Hardin_ Jun 12 2012