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 A212733 Number of 0..2 arrays of length 2*n+3 with sum less than 2*n in any length 2n subsequence (=less than 50% duty cycle) 1

%I

%S 13,322,4057,43050,428617,4135249,39179582,366956550,3410099667,

%T 31512792243,290000751576,2660274782385,24342553658646,

%U 222296998969810,2026699958947573,18452534543569730,167814036979752705

%N Number of 0..2 arrays of length 2*n+3 with sum less than 2*n in any length 2n subsequence (=less than 50% duty cycle)

%C Row 4 of A212729

%H R. H. Hardin, <a href="/A212733/b212733.txt">Table of n, a(n) for n = 1..210</a>

%F From _Vaclav Kotesovec_, Jul 31 2013: (Start)

%F Empirical: n*(2*n-1)*(641952*n^5 - 9661256*n^4 + 56355290*n^3 - 158324563*n^2 + 212843323*n - 108787536)*a(n) = (24394176*n^7 - 397299472*n^6 + 2605594692*n^5 - 8806725568*n^4 + 16309249503*n^3 - 16218569485*n^2 + 7794486684*n - 1330045920)*a(n-1) - 9*(14122944*n^7 - 240151568*n^6 + 1667254836*n^5 - 6073887920*n^4 + 12400532871*n^3 - 13948629407*n^2 + 7754485194*n - 1524164040)*a(n-2) + 81*(n-4)*(2*n-7)*(641952*n^5 - 6451496*n^4 + 24129786*n^3 - 40806709*n^2 + 29824803*n - 6932790)*a(n-3)

%F Conjecture: a(n) ~ 27/2*9^n. (End)

%e Some solutions for n=3

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

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

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

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ May 25 2012

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Last modified March 24 08:26 EDT 2023. Contains 361455 sequences. (Running on oeis4.)