|
%I #8 Dec 20 2018 10:16:59
%S 33,68,154,352,798,1804,4086,9304,21194,48176,109506,249120,566754,
%T 1289056,2931842,6668688,15168650,34502104,78476674,178499728,
%U 406009530,923494792,2100545026,4777818256,10867446266,24718685528,56224184050
%N Number of (n+2) X (1+2) 0..1 arrays with no 3 x 3 subblock diagonal sum 0 or 1 and no antidiagonal sum 0 or 1 and no row sum 1 and no column sum 1.
%H R. H. Hardin, <a href="/A256022/b256022.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -2*a(n-6) -4*a(n-7) +2*a(n-9) for n>10.
%F Empirical g.f.: x*(33 + 2*x + 51*x^2 - 20*x^3 - 24*x^4 - 56*x^5 - 66*x^6 + 12*x^7 + 36*x^8 + 2*x^9) / ((1 - x)*(1 - x - 4*x^3 - 4*x^4 - 4*x^5 - 2*x^6 + 2*x^7 + 2*x^8)). - _Colin Barker_, Dec 20 2018
%e Some solutions for n=4:
%e ..1..0..1....0..1..1....0..1..1....1..1..0....0..1..1....1..1..1....1..1..1
%e ..1..1..1....1..1..0....1..1..1....1..1..1....1..1..1....1..0..1....1..1..1
%e ..1..1..0....1..1..1....1..0..1....1..1..1....1..1..1....1..1..1....1..0..1
%e ..0..1..1....1..1..1....1..1..1....1..1..0....0..1..1....1..1..0....1..1..1
%e ..1..1..1....0..1..1....1..1..1....0..1..1....1..1..1....0..1..1....0..1..1
%e ..1..0..1....1..1..1....1..0..1....1..1..1....1..0..1....1..0..1....1..1..0
%Y Column 1 of A256029.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 13 2015
| 