A296684 - OEIS

%I #7 Dec 18 2017 22:45:17

%S 7,145,1162,11478,121477,1210458,12227803,124103052,1254382781,

%T 12689916581,128420744670,1299239741961,13145213613487,

%U 133001572025151,1345666857760526,13615069768087393,137753603402933018

%N Number of nX4 0..1 arrays with each 1 adjacent to 1, 2 or 3 king-move neighboring 1s.

%C Column 4 of A296688.

%H R. H. Hardin, <a href="/A296684/b296684.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A296684/a296684.pdf">Maple-assisted proof of formula</a>

%F Empirical: a(n) = 7*a(n-1) +15*a(n-2) +181*a(n-3) -141*a(n-4) +269*a(n-5) -2149*a(n-6) -2006*a(n-7) -3785*a(n-8) -973*a(n-9) +8803*a(n-10) +516*a(n-11) -2504*a(n-12) +3529*a(n-13) -5347*a(n-14) +1719*a(n-15) +3063*a(n-16) -2485*a(n-17) -404*a(n-18) -697*a(n-19) +572*a(n-20) +47*a(n-21) +143*a(n-22) +82*a(n-23) -100*a(n-24) -10*a(n-25) +4*a(n-26).

%F Empirical formula confirmed by _Robert Israel_, Dec 18 2017: see link.

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A296688.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 18 2017