A188820 - OEIS

%I #10 Apr 29 2018 09:03:44

%S 32,169,432,841,1360,2025,2800,3721,4752,5929,7216,8649,10192,11881,

%T 13680,15625,17680,19881,22192,24649,27216,29929,32752,35721,38800,

%U 42025,45360,48841,52432,56169,60016,64009,68112,72361,76720,81225,85840,90601

%N Number of n X 5 binary arrays without the pattern 0 1 diagonally or antidiagonally.

%C Column 5 of A188824.

%H R. H. Hardin, <a href="/A188820/b188820.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>5.

%F Conjectures from _Colin Barker_, Apr 29 2018: (Start)

%F G.f.: x*(32 + 105*x + 94*x^2 + 41*x^3 - 16*x^4) / ((1 - x)^3*(1 + x)).

%F a(n) = 9 - 48*n + 64*n^2 for n even.

%F a(n) = -48*n + 64*n^2 for n>1 and odd.

%F (End)

%e Some solutions for 3 X 5:

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

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

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

%Y Cf. A188824.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 11 2011