A272965 T(n,k) = Number of n X k 0..1 arrays with exactly n+k-1 having value 1 and no three 1's forming an isosceles right triangle.

1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 9, 0, 9, 0, 1, 1, 1, 6, 8, 8, 6, 1, 1, 1, 0, 16, 8, 12, 8, 16, 0, 1, 1, 1, 66, 71, 58, 58, 71, 66, 1, 1, 1, 0, 95, 212, 367, 192, 367, 212, 95, 0, 1, 1, 1, 177, 731, 1952, 838, 838, 1952, 731, 177, 1, 1, 1, 0, 493, 1840, 10854

Offset

1,24

Comments

Table starts

.1.1..1...1.....1.....1......1......1......1......1.......1......1.....1....1.1

.1.0..1...0.....1.....0......1......0......1......0.......1......0.....1....0.1

.1.1..0...1.....9.....6.....16.....66.....95....177.....493...1153..2238.5011

.1.0..1...0.....8.....8.....71....212....731...1840....5953..18632.54705

.1.1..9...8....12....58....367...1952..10854..28952..111036.509073

.1.0..6...8....58...192....838...4968..37436.250516.1268025

.1.1.16..71...367...838...4892..26051.198970

.1.0.66.212..1952..4968..26051.230268

.1.1.95.731.10854.37436.198970

Links

R. H. Hardin, Table of n, a(n) for n = 1..126

Formula

Empirical for column k:

k=1: a(n) = a(n-1);

k=2: a(n) = a(n-2);

k=3: a(n) = [linear recurrence of order 32].

Example

Some solutions for n=6, k=4
..1..1..1..1. .1..1..0..1. .0..1..1..1. .1..1..1..1. .1..0..1..1
..0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..0. .1..0..0..0
..0..0..0..0. .0..0..1..0. .0..0..1..0. .0..0..0..0. .0..1..0..0
..0..0..1..0. .0..1..0..0. .0..1..0..0. .0..1..0..0. .0..0..1..0
..0..0..0..1. .0..0..0..0. .1..0..0..0. .1..0..0..0. .0..0..0..0
..1..1..0..1. .1..1..1..0. .1..0..1..1. .1..0..1..1. .0..1..1..1

Crossrefs

Sequence in context: A340879 A086199 A167545 * A059058 A343587 A021015

Adjacent sequences: A272962 A272963 A272964 * A272966 A272967 A272968

Keyword

nonn,tabl

Author

R. H. Hardin, May 11 2016

Status

approved