A278772 Number of n X 2 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly two mistakes.

0, 2, 20, 117, 503, 1750, 5209, 13751, 33000, 73282, 152581, 300872, 566293, 1023724, 1786462, 3021818, 4971616, 7978746, 12521114, 19254543, 29066411, 43142066, 63046335, 90822745, 129113400, 181302810, 251689347, 345688410, 470071817

Offset: 1

Author

R. H. Hardin, Nov 28 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 2 of A278778.

Formula

Empirical: a(n) = (1/3628800)*n^10 + (1/80640)*n^9 + (1/3780)*n^8 + (17/8064)*n^7 + (1513/172800)*n^6 + (167/11520)*n^5 + (12329/362880)*n^4 + (197/4032)*n^3 - (2167/50400)*n^2 - (11/168)*n.

Conjectures from Colin Barker, Feb 10 2019: (Start)

G.f.: x^2*(2 - 2*x + 7*x^2 - 14*x^3 + 12*x^4 - 5*x^5 + x^6) / (1 - x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.

(End)