cp's OEIS Frontend

A183342 T(n,k)=Number of nXk binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.

%I A183342 #7 Jul 22 2025 08:50:14
%S A183342 1,1,1,1,2,1,1,3,3,1,1,4,5,4,1,1,6,7,7,6,1,1,9,13,12,13,9,1,1,13,23,
%T A183342 26,26,23,13,1,1,19,37,51,72,51,37,19,1,1,28,63,97,175,175,97,63,28,1,
%U A183342 1,41,109,193,407,513,407,193,109,41,1,1,60,183,380,1005,1397,1397,1005,380
%N A183342 T(n,k)=Number of nXk binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.
%C A183342 Equivalent to all 1s connected only in 2X2 blocks
%C A183342 Table starts
%C A183342 .1..1...1...1....1.....1......1.......1.......1........1.........1..........1
%C A183342 .1..2...3...4....6.....9.....13......19......28.......41........60.........88
%C A183342 .1..3...5...7...13....23.....37......63.....109......183.......309........527
%C A183342 .1..4...7..12...26....51.....97.....193.....380......741......1456.......2860
%C A183342 .1..6..13..26...72...175....407....1005....2450.....5893.....14318......34780
%C A183342 .1..9..23..51..175...513...1397....4133...12075....34521....100047.....290287
%C A183342 .1.13..37..97..407..1397...4531...16029...55471...188735....651517....2246015
%C A183342 .1.19..63.193.1005..4133..16029...68662..286079..1170324...4869491...20218182
%C A183342 .1.28.109.380.2450.12075..55471..286079.1429824..6989477..34856362..173451524
%C A183342 .1.41.183.741.5893.34521.188735.1170324.6989477.40840428.243887497.1451641573
%H A183342 R. H. Hardin, <a href="/A183342/b183342.txt">Table of n, a(n) for n = 1..839</a>
%e A183342 Some solutions for 6X5
%e A183342 ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e A183342 ..0..0..0..0..0....0..0..1..1..0....1..1..0..0..0....0..0..0..0..0
%e A183342 ..0..0..1..1..0....0..0..1..1..0....1..1..0..0..0....0..0..0..0..0
%e A183342 ..0..0..1..1..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e A183342 ..0..0..0..0..0....1..1..0..0..0....0..0..0..0..0....0..1..1..0..0
%e A183342 ..0..0..0..0..0....1..1..0..0..0....0..0..0..0..0....0..1..1..0..0
%Y A183342 Diagonal is A145857
%Y A183342 Column 2 is A000930(n+1)
%Y A183342 Column 3 is A003229
%K A183342 nonn,tabl
%O A183342 1,5
%A A183342 _R. H. Hardin_ Jan 04 2011