A297720 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 2 or 4 neighboring 1s.

1, 2, 1, 4, 10, 1, 7, 34, 29, 1, 12, 83, 145, 87, 1, 21, 258, 523, 747, 280, 1, 37, 865, 2717, 4212, 4090, 876, 1, 65, 2651, 14462, 36981, 34319, 21116, 2735, 1, 114, 8041, 68919, 336653, 512354, 268630, 110551, 8583, 1, 200, 25114, 332306, 2699832, 8103241

Offset

1,2

Comments

Table starts

.1.....2.......4.........7..........12............21..............37

.1....10......34........83.........258...........865............2651

.1....29.....145.......523........2717.........14462...........68919

.1....87.....747......4212.......36981........336653.........2699832

.1...280....4090.....34319......512354.......8103241.......107787351

.1...876...21116....268630.....6812856.....183324631......4021047904

.1..2735..110551...2139403....91994155....4238895126....154327332017

.1..8583..582755..17031173..1242370107...98184350818...5920531350715

.1.26900.3055652.135252357.16741579726.2265008802005.226188909640209

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 13]

k=4: [order 42]

k=5: [order 87]

Empirical for row n:

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

n=2: a(n) = 4*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4) -24*a(n-5) +24*a(n-6)

n=3: [order 18]

n=4: [order 51]

Example

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

Crossrefs

Column 2 is A295525.

Row 1 is A005251(n+2).

Sequence in context: A100229 A071949 A297506 * A297654 A220922 A220993

Adjacent sequences: A297717 A297718 A297719 * A297721 A297722 A297723

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 04 2018

Status

approved