A296551 - OEIS

%I #8 Feb 23 2019 07:24:01

%S 1,1,4,7,11,18,34,59,100,174,309,538,930,1620,2835,4941,8596,14980,

%T 26129,45536,79328,138252,240988,419984,731872,1275492,2222988,

%U 3874156,6751645,11766605,20506721,35738549,62283936,108546855,189173003,329685682

%N Number of n X 5 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 3 or 6 neighboring 1s.

%H R. H. Hardin, <a href="/A296551/b296551.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 3*a(n-4) + a(n-6) + 3*a(n-7) + a(n-10).

%F Empirical g.f.: x*(1 + 3*x^2 + 3*x^3 + x^4 + 4*x^5 + 3*x^6 + x^8 + x^9) / ((1 + x)*(1 - x + x^2)*(1 - x - x^3 - 2*x^4 - x^7)). - _Colin Barker_, Feb 23 2019

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 5 of A296554.

%K nonn

%O 1,3

%A _R. H. Hardin_, Dec 15 2017