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A269078 Number of 4 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once. 1

%I #8 Jan 19 2019 02:40:52

%S 16,89,537,3288,17713,102545,542112,2991561,15699273,84015848,

%T 437869217,2298582593,11896438960,61665786297,317089210745,

%U 1629210973432,8329629544721,42518834195697,216316340106688,1098583548812969

%N Number of 4 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once.

%H R. H. Hardin, <a href="/A269078/b269078.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 28*a(n-2) - 78*a(n-3) - 264*a(n-4) + 296*a(n-5) + 527*a(n-6) - 252*a(n-7) - 324*a(n-8).

%F Empirical g.f.: x*(16 + 25*x - 267*x^2 - 104*x^3 + 691*x^4 + 275*x^5 - 576*x^6 - 324*x^7) / (1 - 2*x - 16*x^2 + 7*x^3 + 18*x^4)^2. - _Colin Barker_, Jan 19 2019

%e Some solutions for n=4:

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

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

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

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

%Y Row 4 of A269075.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 19 2016

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Last modified March 3 14:40 EST 2024. Contains 370512 sequences. (Running on oeis4.)