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A202937 Number of (n+3) X 9 binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column. 1

%I

%S 194481,359970,695114,1360328,2631416,4958318,9044252,15949741,

%T 27226555,45087162,72615870,114028454,174987698,262982942,387782408,

%U 561967787,801561301,1126756210,1562762514,2140780404,2899114844,3884445518

%N Number of (n+3) X 9 binary arrays with consecutive windows of four bits considered as a binary number nondecreasing in every row and column.

%C Column 6 of A202939.

%H R. H. Hardin, <a href="/A202937/b202937.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/15120)*n^9 + (1/96)*n^8 + (235/504)*n^7 + (725/72)*n^6 + 125*n^5 + (276005/288)*n^4 + (13991149/3024)*n^3 + (1320845/72)*n^2 + (24830539/420)*n + 111295.

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

%F G.f.: x*(194481 - 1584840*x + 5847059*x^2 - 12729882*x^3 + 17952876*x^4 - 16970274*x^5 + 10737942*x^6 - 4382257*x^7 + 1046214*x^8 - 111295*x^9) / (1 - x)^10.

%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

%F (End)

%e Some solutions for n=1:

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

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

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

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

%Y Cf. A202939.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 26 2011

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Last modified January 23 01:30 EST 2020. Contains 331166 sequences. (Running on oeis4.)