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

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

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].

Example

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

Crossrefs

Columns are A000073(n+3), A282990, A282991, A282992, A282993, A282994, A282995.

Diagonal is A067968.

Sequence in context: A282862 A296578 A268750 * A295275 A295253 A295652

Adjacent sequences: A282993 A282994 A282995 * A282997 A282998 A282999

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 26 2017

Status

approved