A231806 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors equal to one

5, 13, 13, 32, 61, 32, 79, 252, 252, 79, 200, 1120, 1699, 1120, 200, 500, 5294, 12044, 12044, 5294, 500, 1249, 23965, 92380, 157633, 92380, 23965, 1249, 3133, 107961, 678081, 2192216, 2192216, 678081, 107961, 3133, 7845, 492274, 4939746, 28305214

Offset

1,1

Comments

Table starts

.....5.......13.........32...........79.............200................500

....13.......61........252.........1120............5294..............23965

....32......252.......1699........12044...........92380.............678081

....79.....1120......12044.......157633.........2192216...........28305214

...200.....5294......92380......2192216........55365917.........1260742591

...500....23965.....678081.....28305214......1260742591........49517022951

..1249...107961....4939746....366087332.....28958572406......1970546390784

..3133...492274...36427030...4826593439....681634049374.....80724891499437

..7845..2241508..268422913..63283320895..15907022844385...3270901271636533

.19640.10179136.1972567930.827033366868.369796154636660.131957283104436587

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +2*a(n-2) +5*a(n-3) -2*a(n-5) -4*a(n-6)

k=2: [order 20]

k=3: [order 45]

Example

Some solutions for n=4 k=4
..0..0..1..0..1....0..0..1..0..0....0..0..0..1..0....0..1..0..1..0
..0..1..0..0..0....1..0..0..0..0....0..1..0..0..0....0..0..0..0..0
..1..0..0..0..1....1..0..0..1..1....0..1..1..0..0....0..0..0..0..0
..1..0..0..0..1....0..1..0..0..0....0..0..1..0..1....0..1..0..0..1
..0..0..0..0..1....0..0..1..0..0....0..0..0..0..0....1..0..0..0..0

Crossrefs

Sequence in context: A235337 A151994 A321992 * A183782 A341751 A244435

Adjacent sequences: A231803 A231804 A231805 * A231807 A231808 A231809

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 13 2013

Status

approved