A188841 - OEIS

%I #9 May 01 2018 05:36:11

%S 128,987,3280,7753,15504,28101,47652,76912,119416,179630,263120,

%T 376740,528840,729495,990756,1326924,1754848,2294248,2968064,3802832,

%U 4829088,6081801,7600836,9431448,11624808,14238562,17337424,20993804,25288472

%N Number of n X 7 binary arrays without the pattern 0 1 diagonally or vertically.

%C Column 7 of A188843.

%H R. H. Hardin, <a href="/A188841/b188841.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (1/5040)*n^7 + (1/72)*n^6 + (143/360)*n^5 + (53/9)*n^4 + (33667/720)*n^3 + (12679/72)*n^2 + (9439/70)*n - 572 for n>4.

%F Empirical g.f.: x*(128 - 37*x - 1032*x^2 + 1981*x^3 - 992*x^4 - 605*x^5 + 700*x^6 - 58*x^7 - 96*x^8 + 3*x^9 + 8*x^10 + x^11) / (1 - x)^8. - _Colin Barker_, May 01 2018

%e Some solutions for 3 X 7:

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

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

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

%Y Cf. A188843.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2011