|
%I #11 Oct 21 2023 09:46:07
%S 7,33,164,811,4035,19997,99245,492401,2443097,12121712,60143345,
%T 298407987,1480586061,7346099129,36448521869,180843564461,
%U 897276298340,4451940313371,22088817679653,109596228179271,543774384192739
%N Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1 or 4 1s.
%C Column 3 of A295275.
%H R. H. Hardin, <a href="/A295270/b295270.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A295270/a295270.pdf">Maple-assisted proof of formula</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2, 10, 20, 17, -1, -9, -12, -1, -1, 1).
%F Empirical: a(n) = 2*a(n-1) + 10*a(n-2) + 20*a(n-3) + 17*a(n-4) - a(n-5) - 9*a(n-6) - 12*a(n-7) - a(n-8) - a(n-9) + a(n-10).
%F Empirical formula is true: see link. - _Robert Israel_, Nov 19 2017
%e Some solutions for n=7:
%e 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0
%e 1 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 0
%e 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1
%e 1 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0
%e 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0
%e 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0
%e 0 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0
%Y Cf. A295275.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 19 2017
| 