A208286 - OEIS

%I #8 Jun 29 2018 14:18:35

%S 42,1764,14946,70216,239490,665892,1604862,3478160,6942474,12974340,

%T 22973082,38883480,63339874,99833412,152904150,228359712,333522218,

%U 477505188,671522130,929228520,1267098882,1704840676,2265846702

%N Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

%C Column 7 of A208287.

%H R. H. Hardin, <a href="/A208286/b208286.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (61/180)*n^7 + (121/20)*n^6 + (1157/36)*n^5 + (425/12)*n^4 - (2923/90)*n^3 - (22/15)*n^2 + 2*n.

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

%F G.f.: 2*x*(21 + 714*x + 1005*x^2 - 1156*x^3 + 203*x^4 + 86*x^5 - 19*x^6) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208287.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 25 2012