A227382 Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having a sum of one, with rows and columns of the latter in lexicographically nondecreasing order.

4, 15, 54, 185, 587, 1704, 4532, 11126, 25430, 54568, 110768, 214130, 396492, 706695, 1217599, 2035257, 3310713, 5254953, 8157605, 12410055, 18533721, 27214306, 39342934, 56065160, 78838936, 109502710, 150354934, 204246360, 274686610

Offset: 1

Author

R. H. Hardin, Jul 09 2013

Keywords

• nonn

Examples

			Some solutions for n=4:
..1..0..0....1..0..0....0..0..0....0..0..0....0..0..0....0..1..0....0..0..1
..0..0..0....0..1..0....0..0..0....0..0..1....1..0..0....1..0..0....0..0..0
..0..1..1....0..1..0....1..0..0....0..0..0....0..0..1....0..0..1....0..0..0
..0..0..0....0..0..1....0..1..1....0..1..0....0..0..1....0..1..0....1..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Crossrefs

Column 3 of A227385.

Formula

Empirical: a(n) = (1/90720)*n^9 + (1/5760)*n^8 + (1/864)*n^7 + (1/64)*n^6 - (91/864)*n^5 + (2563/1920)*n^4 - (96743/18144)*n^3 + (5083/288)*n^2 - (10643/360)*n + 31 for n>3.

Conjectures from Colin Barker, Sep 08 2018: (Start)

G.f.: x*(4 - 25*x + 84*x^2 - 160*x^3 + 207*x^4 - 179*x^5 + 107*x^6 - 42*x^7 + 19*x^9 - 16*x^10 + 6*x^11 - x^12) / (1 - x)^10.

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>13.

(End)