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

1,1

Links

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

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)

Example

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

Crossrefs

Column 3 of A227385.

Sequence in context: A370034 A289927 A164619 * A090326 A291032 A006234

Adjacent sequences: A227379 A227380 A227381 * A227383 A227384 A227385

Keyword

nonn

Author

R. H. Hardin, Jul 09 2013

Status

approved