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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.
1
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
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 A372452
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 11 2016
STATUS
approved