A300776 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 4, 3, 4, 0, 0, 9, 11, 11, 9, 0, 0, 19, 32, 36, 32, 19, 0, 0, 41, 102, 179, 179, 102, 41, 0, 0, 88, 330, 735, 1536, 735, 330, 88, 0, 0, 189, 1059, 3482, 10374, 10374, 3482, 1059, 189, 0, 0, 406, 3418, 15986, 78932, 116954, 78932, 15986, 3418

Offset

1,8

Comments

Table starts

.0...0....0.....0.......0.........0...........0............0..............0

.0...1....2.....4.......9........19..........41...........88............189

.0...2....3....11......32.......102.........330.........1059...........3418

.0...4...11....36.....179.......735........3482........15986..........74347

.0...9...32...179....1536.....10374.......78932.......592064........4449947

.0..19..102...735...10374....116954.....1413931.....17336190......210669938

.0..41..330..3482...78932...1413931....27354464....538564737....10457318118

.0..88.1059.15986..592064..17336190...538564737..16992197390...534677180915

.0.189.3418.74347.4449947.210669938.10457318118.534677180915.27071152148341

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

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

k=3: [order 15]

k=4: [order 56] for n>57

Example

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

Crossrefs

Column 2 is A078039(n-2).

Sequence in context: A179011 A300465 A300646 * A301400 A134315 A268584

Adjacent sequences: A300773 A300774 A300775 * A300777 A300778 A300779

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 12 2018

Status

approved