A227555 Number of n X 3 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 4 binary array having nonzero determinant, with rows and columns of the latter in lexicographically nondecreasing order.

7, 33, 147, 585, 2080, 6653, 19356, 51827, 129090, 301882, 668004, 1407882, 2841813, 5519404, 10355651, 18833130, 33296081, 57369975, 96549697, 159011007, 256713726, 406881423, 633961558, 972192389, 1468928820, 2188909112

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1/2217600)*n^11 - (1/201600)*n^10 + (1/3780)*n^9 - (9/4480)*n^8 + (6403/201600)*n^7 - (4609/28800)*n^6 + (4331/4032)*n^5 - (40753/13440)*n^4 + (1339067/151200)*n^3 - (443809/50400)*n^2 + (83507/9240)*n.

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

G.f.: x*(7 - 51*x + 213*x^2 - 541*x^3 + 967*x^4 - 1246*x^5 + 1197*x^6 - 848*x^7 + 439*x^8 - 150*x^9 + 31*x^10) / (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>12.

(End)

Example

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

Crossrefs

Column 3 of A227558.

Sequence in context: A225895 A089106 A211829 * A304278 A155603 A282991

Adjacent sequences: A227552 A227553 A227554 * A227556 A227557 A227558

Keyword

nonn

Author

R. H. Hardin, Jul 16 2013

Status

approved