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

1,2

Links

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

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)

Example

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

Crossrefs

Column 2 of A278778.

Sequence in context: A084894 A203238 A061004 * A213432 A219837 A219759

Adjacent sequences: A278769 A278770 A278771 * A278773 A278774 A278775

Keyword

nonn

Author

R. H. Hardin, Nov 28 2016

Status

approved