A272973 T(n,k)=Number of nXk 0..1 arrays with exactly n+k-2 having value 1 and no three 1s forming an isosceles triangle.

1, 2, 2, 3, 6, 3, 4, 10, 10, 4, 5, 21, 12, 21, 5, 6, 14, 4, 4, 14, 6, 7, 28, 14, 8, 14, 28, 7, 8, 18, 36, 4, 4, 36, 18, 8, 9, 29, 23, 37, 4, 37, 23, 29, 9, 10, 22, 44, 8, 4, 4, 8, 44, 22, 10, 11, 32, 14, 44, 10, 8, 10, 44, 14, 32, 11, 12, 26, 48, 8, 80, 4, 4, 80, 8, 48, 26, 12, 13, 36, 14, 44

Offset

1,2

Comments

Table starts

..1..2..3..4..5..6..7..8..9.10.11..12.13.14.15.16.17

..2..6.10.21.14.28.18.29.22.32.26..36.30.40.34.44

..3.10.12..4.14.36.23.44.14.48.14..52.14.56.16

..4.21..4..8..4.37..8.44..8.44..0..34..4.44

..5.14.14..4..4..4.10.80.37.56..4..12..0

..6.28.36.37..4..8..4.22..0.34.32.203

..7.18.23..8.10..4..4..4..2.48.24

..8.29.44.44.80.22..4..8.16

..9.22.14..8.37..0..2.16

.10.32.48.44.56.34.48

.11.26.14..0..4.32

.12.36.52.34.12

.13.30.14..4

.14.40.56

.15.34

.16

Links

R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) -a(n-2)

k=2: a(n) = a(n-1) +a(n-2) -a(n-3) for n>11

Example

All solutions for n=3 k=4
..0..0..0..1. .1..0..0..0. .1..1..1..0. .0..1..1..1
..0..0..0..1. .1..0..0..0. .0..0..0..1. .1..0..0..0
..1..1..1..0. .0..1..1..1. .0..0..0..1. .1..0..0..0

Crossrefs

Sequence in context: A322744 A128228 A190098 * A272958 A290632 A291543

Adjacent sequences: A272970 A272971 A272972 * A272974 A272975 A272976

Keyword

nonn,tabl

Author

R. H. Hardin, May 11 2016

Status

approved