A208311 - OEIS

%I #8 Jul 02 2018 04:53:52

%S 16,162,1446,12474,106488,906120,7702668,65459016,556238664,

%T 4726531278,40162523382,341270401878,2899853256528,24640717614786,

%U 209377814555934,1779131166029946,15117684272558352,128458419414226920

%N Number of n X 5 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

%C Column 5 of A208314.

%H R. H. Hardin, <a href="/A208311/b208311.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 17*a(n-1) - 105*a(n-2) + 354*a(n-3) - 756*a(n-4) + 1062*a(n-5) - 945*a(n-6) + 459*a(n-7) - 81*a(n-8).

%F Empirical g.f.: 2*x*(8 - 55*x + 186*x^2 - 381*x^3 + 504*x^4 - 405*x^5 + 162*x^6 - 27*x^7) / ((1 - 3*x + 3*x^2)*(1 - 14*x + 60*x^2 - 132*x^3 + 180*x^4 - 126*x^5 + 27*x^6)). - _Colin Barker_, Jul 02 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208314.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 25 2012