|
%I #8 Jun 15 2018 07:59:34
%S 72,93,218,471,932,1725,3011,5014,8016,12385,18572,27141,38768,54273,
%T 74621,100956,134604,177109,230238,296019,376748,475029,593783,736290,
%U 906200,1107577,1344912,1623169,1947800,2324793,2760689,3262632,3838388
%N Number of (n+1) X 6 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.
%C Column 5 of A206267.
%H R. H. Hardin, <a href="/A206264/b206264.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) - 14*a(n-2) + 14*a(n-3) - 14*a(n-5) + 14*a(n-6) - 6*a(n-7) + a(n-8) for n>9.
%F Conjectures from _Colin Barker_, Jun 15 2018: (Start)
%F G.f.: x*(72 - 339*x + 668*x^2 - 543*x^3 - 144*x^4 + 683*x^5 - 591*x^6 + 232*x^7 - 36*x^8) / ((1 - x)^7*(1 + x)).
%F a(n) = (11520 + 8028*n + 5104*n^2 + 1665*n^3 + 295*n^4 + 27*n^5 + n^6) / 720 for n>1 and even.
%F a(n) = (10800 + 8028*n + 5104*n^2 + 1665*n^3 + 295*n^4 + 27*n^5 + n^6) / 720 for n>1 and odd.
%F (End)
%e Some solutions for n=4:
%e ..1..0..1..0..1..0....1..1..1..1..0..0....0..1..0..1..0..1....0..0..0..0..0..0
%e ..0..1..0..1..0..1....0..0..0..0..0..0....1..0..1..0..1..0....0..0..0..0..0..0
%e ..1..0..1..0..1..0....0..0..0..0..0..0....0..1..0..1..0..1....0..0..0..0..0..0
%e ..0..1..0..1..0..1....0..0..0..0..0..0....1..0..1..0..1..0....0..0..0..0..0..0
%e ..1..0..1..0..1..1....0..0..0..0..0..0....0..1..0..1..0..1....0..0..0..0..0..0
%Y Cf. A206267.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 05 2012
| 