A272958 T(n,k)=Number of nXk 0..1 arrays with exactly n+k-2 having value 1 and no three 1s forming an isosceles right triangle.

1, 2, 2, 3, 6, 3, 4, 10, 10, 4, 5, 21, 24, 21, 5, 6, 34, 24, 24, 34, 6, 7, 62, 107, 60, 107, 62, 7, 8, 100, 236, 210, 210, 236, 100, 8, 9, 171, 499, 637, 768, 637, 499, 171, 9, 10, 276, 1228, 1840, 1898, 1898, 1840, 1228, 276, 10, 11, 458, 2753, 5792, 8211, 7468, 8211, 5792

Offset

1,2

Comments

Table starts

.1...2....3.....4......5......6.......7.......8.......9......10.......11

.2...6...10....21.....34.....62.....100.....171.....276.....458......740

.3..10...24....24....107....236.....499....1228....2753....6292....14751

.4..21...24....60....210....637....1840....5792...18556...54034...160246

.5..34..107...210....768...1898....8211...37402..192579..635086..2366644

.6..62..236...637...1898...7468...26052..138476..831738.4677062.23090612

.7.100..499..1840...8211..26052..131056..648178.4336294

.8.171.1228..5792..37402.138476..648178.4614732

.9.276.2753.18556.192579.831738.4336294

Links

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

Formula

Empirical for column k:

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

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

k=3: [order 72]

Example

Some solutions for n=5 k=4
..0..0..1..1. .1..1..0..0. .1..1..1..0. .1..0..0..1. .0..1..0..1
..0..1..0..0. .0..0..0..0. .0..0..0..0. .1..0..0..0. .0..1..0..1
..1..0..0..1. .1..0..0..1. .0..1..0..0. .0..0..0..1. .0..0..0..0
..0..0..0..1. .0..1..0..0. .0..0..1..0. .0..0..1..0. .0..0..0..0
..0..0..0..1. .0..0..1..1. .1..0..0..1. .1..0..1..0. .1..1..1..0

Crossrefs

Sequence in context: A128228 A190098 A272973 * A290632 A291543 A296320

Adjacent sequences: A272955 A272956 A272957 * A272959 A272960 A272961

Keyword

nonn,tabl

Author

R. H. Hardin, May 11 2016

Status

approved