A297221 - OEIS

%I #8 Feb 26 2019 12:05:54

%S 6,33,182,997,5570,30946,171851,955316,5308160,29497088,163916530,

%T 910869797,5061672943,28127490455,156303166524,868569845751,

%U 4826603668246,26821221189069,149044329620412,828232684722634

%N Number of n X 5 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 neighboring 1s.

%H R. H. Hardin, <a href="/A297221/b297221.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 16*a(n-2) + 45*a(n-3) + 39*a(n-4) - 3*a(n-5) - 21*a(n-6) + 8*a(n-7) - 4*a(n-8) + a(n-9).

%F Empirical g.f.: x*(6 + 27*x + 53*x^2 + 17*x^3 - 58*x^4 - 35*x^5 + 47*x^6 - 13*x^7 + x^8) / ((1 + 2*x + x^2 - x^3)*(1 - 3*x - 11*x^2 - 19*x^3 + 7*x^4 - 3*x^5 + x^6)). - _Colin Barker_, Feb 26 2019

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 5 of A297224.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 27 2017