A260015 T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000101 00010101 or 01010101

36, 49, 49, 109, 98, 109, 209, 252, 252, 209, 436, 578, 889, 578, 436, 828, 1232, 2492, 2492, 1232, 828, 1744, 2738, 6944, 8450, 6944, 2738, 1744, 3344, 6262, 18356, 25600, 25600, 18356, 6262, 3344, 7005, 14112, 56137, 84050, 87024, 84050, 56137, 14112

Offset

1,1

Comments

Table starts

....36....49.....109......209......436.......828.......1744........3344

....49....98.....252......578.....1232......2738.......6262.......14112

...109...252.....889.....2492.....6944.....18356......56137......155304

...209...578....2492.....8450....25600.....84050.....292422......985608

...436..1232....6944....25600....87024....294336....1231648.....4380288

...828..2738...18356....84050...294336...1210568....5674360....24724512

..1744..6262...56137...292422..1231648...5674360...33390411...166527544

..3344.14112..155304...985608..4380288..24724512..166527544..1002982472

..7005.31500..457083..3251280.16773440.101249348..840032861..5561958496

.13424.70688.1237656.10857800.58243968.428893472.4030790792.32495162312

Links

R. H. Hardin, Table of n, a(n) for n = 1..880

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-2) +7*a(n-4) +a(n-5) +2*a(n-6) +a(n-7) -a(n-8) +a(n-9) for n>10

k=2: a(n) = 2*a(n-1) +a(n-3) +3*a(n-4) -5*a(n-5) -a(n-6) -a(n-8) +a(n-9) for n>10

k=3: a(n) = 4*a(n-2) +37*a(n-4) -13*a(n-6) -124*a(n-8) +12*a(n-10) +72*a(n-12) for n>13

k=4: [order 16] for n>17

k=5: [order 18] for n>21

k=6: [order 36] for n>37

k=7: [order 56] for n>57

Example

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

Crossrefs

Sequence in context: A349869 A260920 A132956 * A374936 A163244 A260008

Adjacent sequences: A260012 A260013 A260014 * A260016 A260017 A260018

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 13 2015

Status

approved