A296015 - OEIS

%I #9 Dec 04 2017 02:55:31

%S 4,28,91,366,1644,6545,26865,112345,461363,1902251,7867396,32451301,

%T 133919803,552939041,2282127828,9419468870,38881999590,160489339983,

%U 662439317422,2734335195143,11286359484536,46586079223617

%N Number of n X 4 0..1 arrays with each 1 adjacent to 1 or 4 king-move neighboring 1s.

%C Column 4 of A296019.

%H R. H. Hardin, <a href="/A296015/b296015.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A296015/a296015.pdf">Maple-assisted proof of formula</a>

%F Empirical: a(n) = a(n-1) + 6*a(n-2) + 36*a(n-3) + 8*a(n-4) - 71*a(n-5) - 345*a(n-6) - 221*a(n-7) + 167*a(n-8) + 1167*a(n-9) + 930*a(n-10) + 200*a(n-11) - 1607*a(n-12) - 1327*a(n-13) - 670*a(n-14) + 1036*a(n-15) + 741*a(n-16) + 514*a(n-17) - 306*a(n-18) - 128*a(n-19) - 114*a(n-20) + 40*a(n-21).

%F Empirical formula confirmed by _Robert Israel_, Dec 03 2017 (see link).

%e Some solutions for n=5:

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

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

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

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

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

%Y Cf. A296019.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 02 2017