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Number of (n+3) X 8 binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column.
1

%I #9 Jun 03 2018 07:57:36

%S 160000,273683,481798,857408,1515902,2631416,4457228,7350643,11802908,

%T 18474721,28237922,42223978,61879898,89032238,125959880,175476293,

%U 241022008,326768063,437731198,579901604,760384054,987553268,1271224388

%N Number of (n+3) X 8 binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column.

%C Column 5 of A202939.

%H R. H. Hardin, <a href="/A202936/b202936.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/1680)*n^8 + (17/210)*n^7 + (134/45)*n^6 + (256/5)*n^5 + (352481/720)*n^4 + (55381/20)*n^3 + (32201731/2520)*n^2 + (19670981/420)*n + 97073.

%F Conjectures from _Colin Barker_, Jun 03 2018: (Start)

%F G.f.: x*(160000 - 1166317*x + 3778651*x^2 - 7066186*x^3 + 8314586*x^4 - 6291988*x^5 + 2987174*x^6 - 812969*x^7 + 97073*x^8) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

%F (End)

%e Some solutions for n=1:

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

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

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

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

%Y Cf. A202939.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 26 2011