A300506 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 3, 5, 2, 2, 5, 8, 3, 4, 3, 8, 13, 6, 7, 7, 6, 13, 21, 6, 6, 20, 6, 6, 21, 34, 11, 17, 32, 32, 17, 11, 34, 55, 26, 34, 68, 56, 68, 34, 26, 55, 89, 43, 57, 191, 208, 208, 191, 57, 43, 89, 144, 82, 80, 504, 546, 1162, 546, 504, 80, 82, 144, 233, 178, 164, 1353, 2006

Offset

1,2

Comments

Table starts

..1..2..3....5....8....13.....21......34.......55........89........144

..2..3..2....3....6.....6.....11......26.......43........82........178

..3..2..4....7....6....17.....34......57.......80.......164........302

..5..3..7...20...32....68....191.....504.....1353......4033......11685

..8..6..6...32...56...208....546....2006.....5835.....18466......58308

.13..6.17...68..208..1162...4067...20265....88836....420674....1978897

.21.11.34..191..546..4067..17412..112660...634311...3789374...21768434

.34.26.57..504.2006.20265.112660.1045409..7841480..64468772..513205097

.55.43.80.1353.5835.88836.634311.7841480.76908966.836417456.8738195507

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) +a(n-2)

k=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) +a(n-5) -2*a(n-6) +a(n-7)

k=3: [order 26] for n>31

k=4: [order 93] for n>103

Example

Some solutions for n=5 k=4
..0..1..0..1. .0..1..0..0. .0..1..0..1. .0..0..0..1. .0..1..0..1
..0..1..1..0. .0..0..0..0. .0..0..1..0. .1..0..0..0. .0..1..1..0
..1..1..0..1. .0..1..1..0. .0..0..0..1. .1..1..0..0. .1..0..1..1
..1..0..0..1. .0..0..0..0. .1..0..0..1. .1..1..0..0. .0..1..1..1
..1..0..0..0. .0..0..1..0. .1..0..0..0. .1..1..1..0. .1..0..0..1

Crossrefs

Column 1 is A000045(n+1).

Sequence in context: A110876 A324019 A275378 * A300888 A300944 A301498

Adjacent sequences: A300503 A300504 A300505 * A300507 A300508 A300509

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 07 2018

Status

approved