A297431 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 neighboring 1s.

1, 1, 1, 1, 2, 1, 1, 7, 3, 1, 1, 12, 14, 4, 1, 1, 18, 26, 22, 6, 1, 1, 33, 43, 42, 68, 9, 1, 1, 73, 109, 105, 183, 163, 13, 1, 1, 139, 301, 349, 535, 513, 320, 19, 1, 1, 244, 649, 1057, 2430, 1673, 1085, 782, 28, 1, 1, 449, 1332, 2834, 12005, 11345, 5108, 3332, 1889, 41, 1, 1

Offset

1,5

Comments

Table starts

.1..1....1....1.....1.......1........1.........1..........1...........1

.1..2....7...12....18......33.......73.......139........244.........449

.1..3...14...26....43.....109......301.......649.......1332........3124

.1..4...22...42...105.....349.....1057......2834.......8216.......24556

.1..6...68..183...535....2430....12005.....45977.....182298......793315

.1..9..163..513..1673...11345....76692....369339....1884628....11192445

.1.13..320.1085..5108...50127...431723...2741816...19713343...158831909

.1.19..782.3332.19690..267505..3338387..28588498..275287217..3091469216

.1.28.1889.9744.66529.1348969.23694911.264853947.3362921639.52055334454

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

Formula

Empirical for column k:

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

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

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

k=4: a(n) = a(n-1) +12*a(n-3) +2*a(n-4) +2*a(n-5) -7*a(n-6) -a(n-7)

k=5: [order 20]

k=6: [order 37]

k=7: [order 81]

Empirical for row n:

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

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

n=3: a(n) = a(n-1) +3*a(n-3) +8*a(n-4) +a(n-5) -a(n-6)

n=4: [order 12]

n=5: [order 29]

n=6: [order 59]

Example

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

Crossrefs

Column 2 is A000930(n+1).

Sequence in context: A178234 A344440 A259175 * A346083 A301922 A144510

Adjacent sequences: A297428 A297429 A297430 * A297432 A297433 A297434

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 30 2017

Status

approved