A278670 Number of n X 2 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly one mistake.

1, 8, 33, 99, 245, 532, 1050, 1926, 3333, 5500, 8723, 13377, 19929, 28952, 41140, 57324, 78489, 105792, 140581, 184415, 239085, 306636, 389390, 489970, 611325, 756756, 929943, 1134973, 1376369, 1659120, 1988712, 2371160, 2813041, 3321528

Offset

1,2

Links

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

Formula

Empirical: a(n) = (1/720)*n^6 + (1/48)*n^5 + (23/144)*n^4 + (19/48)*n^3 + (61/180)*n^2 + (1/12)*n.

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

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

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Column 2 of A278676.

Sequence in context: A014820 A070736 A051836 * A301771 A070051 A087235

Adjacent sequences: A278667 A278668 A278669 * A278671 A278672 A278673

Keyword

nonn

Author

R. H. Hardin, Nov 25 2016

Status

approved