A226867 Number of n X 3 (-1,0,1) arrays of determinants of 2 X 2 subblocks of some (n+1) X 4 binary array with rows and columns of the latter in lexicographically nondecreasing order.

7, 37, 187, 792, 2866, 9136, 26267, 69311, 170084, 392159, 856558, 1784149, 3563340, 6855064, 12751438, 23010044, 40392728, 69146369, 115673477, 189452998, 304286614, 479963424, 744456493, 1136788693, 1710732884, 2539543163

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/2217600)*n^11 - (1/403200)*n^10 + (11/48384)*n^9 - (1/1344)*n^8 + (947/50400)*n^7 + (701/57600)*n^6 - (1447/80640)*n^5 + (7159/2688)*n^4 - (2391281/302400)*n^3 + (1074793/50400)*n^2 - (204143/9240)*n + 14 for n>1.

Conjectures from Colin Barker, Sep 06 2018: (Start)

G.f.: x*(7 - 47*x + 205*x^2 - 550*x^3 + 1029*x^4 - 1353*x^5 + 1280*x^6 - 857*x^7 + 409*x^8 - 136*x^9 + 34*x^10 - 2*x^11 - x^12) / (1 - x)^12.

a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>13.

(End)

Example

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

Crossrefs

Column 3 of A226870.

Sequence in context: A117424 A192811 A037546 * A140476 A057651 A106925

Adjacent sequences: A226864 A226865 A226866 * A226868 A226869 A226870

Keyword

nonn

Author

R. H. Hardin, Jun 20 2013

Status

approved