cp's OEIS Frontend

A297299 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 2 neighboring 1s.

%I A297299 #4 Dec 27 2017 21:13:52
%S A297299 1,1,1,1,1,1,1,2,1,1,1,3,3,1,1,1,4,5,5,1,1,1,6,9,10,8,1,1,1,9,17,21,
%T A297299 19,13,1,1,1,13,32,50,49,36,21,1,1,1,19,60,130,157,114,69,34,1,1,1,28,
%U A297299 113,332,600,495,266,131,55,1,1,1,41,213,840,2161,2816,1574,620,250,89,1,1,1
%N A297299 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 2 neighboring 1s.
%C A297299 Table starts
%C A297299 .1.1..1...1....1.....1......1.......1........1.........1..........1...........1
%C A297299 .1.1..2...3....4.....6......9......13.......19........28.........41..........60
%C A297299 .1.1..3...5....9....17.....32......60......113.......213........401.........755
%C A297299 .1.1..5..10...21....50....130.....332......840......2128.......5408.......13772
%C A297299 .1.1..8..19...49...157....600....2161.....7479.....25639......88307......306281
%C A297299 .1.1.13..36..114...495...2816...14138....64406....288079....1310914.....6040052
%C A297299 .1.1.21..69..266..1574..13504...93906...551477...3159693...18792129...113862870
%C A297299 .1.1.34.131..620..5031..65521..629563..4738693..34652662..269300602..2142898994
%C A297299 .1.1.55.250.1446.16123.319835.4235806.40753529.379882818.3857849537.40317718384
%H A297299 R. H. Hardin, <a href="/A297299/b297299.txt">Table of n, a(n) for n = 1..680</a>
%F A297299 Empirical for column k:
%F A297299 k=1: a(n) = a(n-1)
%F A297299 k=2: a(n) = a(n-1)
%F A297299 k=3: a(n) = a(n-1) +a(n-2)
%F A297299 k=4: a(n) = a(n-1) +2*a(n-2) -a(n-4)
%F A297299 k=5: a(n) = 2*a(n-1) +2*a(n-2) -2*a(n-3) -2*a(n-4) for n>5
%F A297299 k=6: a(n) = 4*a(n-1) -8*a(n-3) -2*a(n-4) +4*a(n-5) +4*a(n-6) +a(n-7) -a(n-8)
%F A297299 k=7: [order 12] for n>14
%F A297299 Empirical for row n:
%F A297299 n=1: a(n) = a(n-1)
%F A297299 n=2: a(n) = a(n-1) +a(n-3)
%F A297299 n=3: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -a(n-4) for n>6
%F A297299 n=4: [order 13] for n>16
%F A297299 n=5: [order 32] for n>37
%F A297299 n=6: [order 68] for n>76
%e A297299 Some solutions for n=5 k=4
%e A297299 ..0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1. .0..1..1..0
%e A297299 ..0..1..1..0. .0..0..0..0. .0..0..0..0. .0..1..1..0. .1..1..0..0
%e A297299 ..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..0
%e A297299 ..0..0..1..1. .0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
%e A297299 ..0..1..1..0. .0..0..0..0. .1..1..0..0. .0..0..0..0. .1..1..0..0
%Y A297299 Column 3 is A000045(n+1).
%Y A297299 Column 4 is A158943(n+1).
%Y A297299 Row 2 is A000930.
%K A297299 nonn,tabl
%O A297299 1,8
%A A297299 _R. H. Hardin_, Dec 27 2017