A278319 Number of n X 2 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

0, 3, 20, 94, 395, 1492, 4991, 14848, 39832, 97835, 223015, 477126, 966849, 1869504, 3470210, 6214384, 10780448, 18178763, 29884150, 48010910, 75541039, 116618372, 176923705, 264148560, 388588200, 563877795, 807899313, 1143890790, 1601794149

Offset: 1

Author

R. H. Hardin, Nov 18 2016

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column 2 of A278325.

Formula

Empirical: a(n) = (1/39916800)*n^11 + (1/725760)*n^10 + (13/362880)*n^9 + (43/120960)*n^8 + (223/172800)*n^7 - (227/34560)*n^6 + (1019/45360)*n^5 + (27263/181440)*n^4 + (12193/113400)*n^3 - (121/840)*n^2 - (13/99)*n.

Conjectures from Colin Barker, Feb 09 2019: (Start)

G.f.: x^2*(3 - 16*x + 52*x^2 - 73*x^3 + 41*x^4 + x^5 - 10*x^6 + 3*x^7) / (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)