A282996 T(n,k) is the number of n X k 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.
2, 4, 4, 7, 11, 7, 13, 33, 33, 13, 24, 98, 163, 98, 24, 44, 291, 803, 803, 291, 44, 81, 865, 3971, 6547, 3971, 865, 81, 149, 2570, 19587, 53389, 53389, 19587, 2570, 149, 274, 7637, 96693, 435027, 720417, 435027, 96693, 7637, 274, 504, 22693, 477297, 3546870
Offset: 1
Examples
Table starts: ...2.....4........7.........13...........24.............44...............81 ...4....11.......33.........98..........291............865.............2570 ...7....33......163........803.........3971..........19587............96693 ..13....98......803.......6547........53389.........435027..........3546870 ..24...291.....3971......53389.......720417........9706901........130854309 ..44...865....19587.....435027......9706901......216173426.......4817792042 ..81..2570....96693....3546870....130854309.....4817792042.....177509416175 .149..7637...477297...28911809...1763845523...107354061547....6539125324144 .274.22693..2355925..235681253..23775564134..2392171690343..240894164469261 .504.67432.11629027.1921212987.320481684651.53305366529469.8874303766960833 Some solutions for n=5 and k=4: ..0..1..1..0. .0..0..1..0. .1..0..0..0. .0..0..0..0. .1..0..0..0 ..0..0..0..1. .0..0..0..1. .0..1..0..0. .1..0..0..0. .0..1..0..1 ..0..1..1..0. .1..0..0..0. .0..1..0..1. .0..1..0..1. .0..0..0..0 ..0..0..0..0. .1..0..0..0. .0..0..1..0. .1..0..1..0. .0..0..0..0 ..0..0..0..1. .0..0..1..0. .1..0..0..1. .0..0..0..0. .0..0..1..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..312
Crossrefs
Formula
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2) +a(n-3);
k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4);
k=3: [order 9];
k=4: [order 15];
k=5: [order 36];
k=6: [order 69].