A297301 - OEIS

%I #10 May 26 2018 08:46:15

%S 1,1,5,10,21,50,130,332,840,2128,5408,13772,35102,89465,227961,580788,

%T 1479748,3770356,9606981,24478804,62372090,158923930,404938148,

%U 1031783666,2628989168,6698674670,17068245866,43489945955,110812526805

%N Number of 4 X n 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 2 neighboring 1s.

%C Row 4 of A297299.

%H R. H. Hardin, <a href="/A297301/b297301.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A297301/a297301.pdf">Maple-assisted proof of empirical formula</a>

%F Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 7*a(n-3) - 4*a(n-4) + 3*a(n-5) + a(n-6) - 5*a(n-7) + 4*a(n-8) - 2*a(n-9) - a(n-10) - 5*a(n-12) - 3*a(n-13) for n > 16.

%F Formula verified by _Robert Israel_, May 25 2018: see link.

%e Some solutions for n=5:

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

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

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

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

%Y Cf. A297299.

%K nonn

%O 1,3

%A _R. H. Hardin_, Dec 27 2017