A227638 Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having determinant equal to one, with rows and columns of the latter in nondecreasing lexicographic order.

3, 11, 39, 127, 377, 1014, 2518, 5844, 12790, 26582, 52769, 100547, 184661, 328068, 565582, 948764, 1552366, 2482688, 3888261, 5973327, 9014649, 13382250, 19564750, 28200044, 40112142, 56355074, 78264849, 107520547, 146215717, 196941352

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/90720)*n^9 - (1/6720)*n^8 + (73/15120)*n^7 - (9/160)*n^6 + (2869/4320)*n^5 - (4367/960)*n^4 + (66841/2835)*n^3 - (41101/560)*n^2 + (17105/126)*n - 108 for n>3.

Conjectures from Colin Barker, Sep 09 2018: (Start)

G.f.: x*(3 - 19*x + 64*x^2 - 128*x^3 + 172*x^4 - 167*x^5 + 151*x^6 - 154*x^7 + 151*x^8 - 107*x^9 + 49*x^10 - 13*x^11 + 2*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:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..0..1....0..0..1
..0..0..1....0..0..0....0..1..1....0..1..0....0..1..0....0..0..0....0..0..0
..0..1..0....1..0..0....1..0..0....0..0..1....0..0..0....0..0..1....1..0..1
..0..1..0....0..0..1....0..1..0....1..0..1....0..1..0....0..0..0....0..0..0

Crossrefs

Column 3 of A227641.

Sequence in context: A112674 A064086 A089579 * A166336 A002783 A289834

Adjacent sequences: A227635 A227636 A227637 * A227639 A227640 A227641

Keyword

nonn

Author

R. H. Hardin, Jul 18 2013

Status

approved