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A227099 Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of two, with rows and columns of the latter in lexicographically nondecreasing order. 1

%I

%S 4,15,48,136,341,771,1606,3133,5789,10214,17315,28342,44977,69437,

%T 104592,154099,222553,315656,440405,605300,820573,1098439,1453370,

%U 1902393,2465413,3165562,4029575,5088194,6376601,7934881,9808516,12048911

%N Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of two, with rows and columns of the latter in lexicographically nondecreasing order.

%H R. H. Hardin, <a href="/A227099/b227099.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/5040)*n^7 + (1/240)*n^6 + (13/720)*n^5 + (5/48)*n^4 + (119/90)*n^3 - (73/120)*n^2 - (2873/420)*n + 23 for n>3.

%F Conjectures from _Colin Barker_, Sep 07 2018: (Start)

%F G.f.: x*(4 - 17*x + 40*x^2 - 52*x^3 + 37*x^4 - 11*x^5 + 2*x^6 - 3*x^7 - x^8 + 3*x^9 - x^10) / (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>11.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A227103.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 01 2013

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Last modified January 27 15:45 EST 2022. Contains 350607 sequences. (Running on oeis4.)