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Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having two adjacent 1's and two adjacent 0's, with rows and columns of the latter in lexicographically nondecreasing order.
1

%I #6 Apr 05 2020 22:14:32

%S 8,34,153,708,3013,11292,37312,110816,301923,766340,1832683,4164473,

%T 9050350,18908103,38136118,74516301,141474093,261645212,472399946,

%U 834253036,1443464344,2450642643,4087839408,6707507638,10837859135

%N Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having two adjacent 1's and two adjacent 0's, with rows and columns of the latter in lexicographically nondecreasing order.

%C Column 3 of A227333.

%H R. H. Hardin, <a href="/A227330/b227330.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/1307674368000)*n^15 + (1/87178291200)*n^14 + (19/7472424960)*n^13 - (1/191600640)*n^12 + (36577/14370048000)*n^11 - (2689/87091200)*n^10 + (436297/365783040)*n^9 - (2115367/121927680)*n^8 + (6669593/23328000)*n^7 - (13770361/4354560)*n^6 + (104682953/3592512)*n^5 - (2364431063/11975040)*n^4 + (366060925289/378378000)*n^3 - (487180400717/151351200)*n^2 + (2320943983/360360)*n - 5585 for n>6.

%e Some solutions for n=4

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Jul 07 2013