A272952 Number of n X 2 0..1 arrays with exactly n+2-2 having value 1 and no three 1s forming an isosceles right triangle.

2, 6, 10, 21, 34, 62, 100, 171, 276, 458, 740, 1211, 1958, 3184, 5150, 8351, 13510, 21880, 35400, 57301, 92712, 150036, 242760, 392821, 635594, 1028442, 1664050, 2692521, 4356586, 7049138, 11405740, 18454911, 29860668, 48315614, 78176300

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) +3*a(n-2) -2*a(n-3) -3*a(n-4) +a(n-5) +a(n-6).

Empirical: a(n) = a(n-1) + a(n-2) + (n+1)(3-(-1)^(n+1))/4. - Chris in the Sequence Fans Mailing List.

Empirical g.f.: x*(2 + 4*x - 2*x^2 - 3*x^3 + x^4 + x^5) / ((1 - x)^2*(1 + x)^2*(1 - x - x^2)). - Colin Barker, Jan 30 2019

Example

Some solutions for n=5:
..1..0. .1..1. .1..1. .0..1. .0..1. .1..0. .1..0. .0..1. .1..0. .0..1
..1..0. .0..0. .0..0. .0..0. .0..1. .1..0. .0..1. .0..1. .0..0. .0..1
..0..1. .0..1. .0..1. .1..1. .0..1. .0..1. .0..1. .1..0. .1..1. .0..1
..0..1. .0..1. .0..0. .0..0. .0..1. .0..0. .1..0. .1..0. .0..0. .0..0
..1..0. .0..1. .1..1. .1..1. .0..1. .1..1. .1..0. .0..1. .1..1. .1..1

Crossrefs

Column 2 of A272958.

Sequence in context: A103628 A207382 A334344 * A034450 A297185 A304991

Adjacent sequences: A272949 A272950 A272951 * A272953 A272954 A272955

Keyword

nonn

Author

R. H. Hardin, May 11 2016

Status

approved