login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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.
8
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 11 2016
STATUS
approved