A202458 - OEIS

%I #8 May 31 2018 14:04:13

%S 1728,4137,9338,19614,38478,71088,124740,209445,338596,529731,805398,

%T 1194128,1731522,2461458,3437424,4723983,6398376,8552269,11293650,

%U 14748882,19064918,24411684,30984636,39007497,48735180,60456903,74499502

%N Number of (n+2) X 7 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.

%C Column 5 of A202461.

%H R. H. Hardin, <a href="/A202458/b202458.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/840)*n^7 + (3/40)*n^6 + (47/30)*n^5 + 16*n^4 + (10847/120)*n^3 + (11557/40)*n^2 + (258737/420)*n + 715.

%F Conjectures from _Colin Barker_, May 31 2018: (Start)

%F G.f.: x*(1728 - 9687*x + 24626*x^2 - 36022*x^3 + 32318*x^4 - 17650*x^5 + 5408*x^6 - 715*x^7) / (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 ..0..0..0..0..1..1..0....0..0..0..0..0..1..0....0..0..0..0..0..0..0

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

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

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

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

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

%Y Cf. A202461.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 19 2011