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A221447 Hilltop maps: number of 2 X n binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or antidiagonal neighbor in a random 0..1 2 X n array. 1

%I #7 Aug 05 2018 08:23:03

%S 1,9,33,117,429,1577,5785,21217,77825,285473,1047145,3841029,14089277,

%T 51680881,189570641,695364065,2550664929,9356094041,34319088593,

%U 125885849013,461761883309,1693788766169,6212986580521,22789856102913

%N Hilltop maps: number of 2 X n binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or antidiagonal neighbor in a random 0..1 2 X n array.

%C Row 2 of A221446.

%H R. H. Hardin, <a href="/A221447/b221447.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + a(n-2) + 5*a(n-3) + a(n-4) + a(n-5) - a(n-6) - a(n-7).

%F Empirical g.f.: x*(1 + 6*x + 5*x^2 + 4*x^3 - x^4 - 2*x^5 - x^6) / ((1 + x^2)*(1 - 3*x - 2*x^2 - 2*x^3 + x^4 + x^5)). - _Colin Barker_, Aug 05 2018

%e Some solutions for n=3:

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

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

%Y Cf. A221446.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 17 2013

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Last modified July 23 08:23 EDT 2024. Contains 374546 sequences. (Running on oeis4.)