A278357 Number of n X 2 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly one mistake.

1, 6, 27, 96, 281, 708, 1590, 3264, 6237, 11242, 19305, 31824, 50661, 78248, 117708, 172992, 249033, 351918, 489079, 669504, 903969, 1205292, 1588610, 2071680, 2675205, 3423186, 4343301, 5467312, 6831501, 8477136, 10450968, 12805760

Offset

1,2

Links

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

Formula

Empirical: a(n) = (1/5040)*n^7 + (1/240)*n^6 + (31/720)*n^5 + (1/16)*n^4 + (41/360)*n^3 + (13/30)*n^2 + (12/35)*n.

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

G.f.: x*(1 - 2*x + 7*x^2 - 8*x^3 + 3*x^4) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Column 2 of A278363.

Sequence in context: A341385 A344100 A136747 * A001940 A320049 A121591

Adjacent sequences: A278354 A278355 A278356 * A278358 A278359 A278360

Keyword

nonn

Author

R. H. Hardin, Nov 19 2016

Status

approved