A295985 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2 or 3 king-move neighboring 1s.

1, 1, 1, 1, 6, 1, 1, 15, 15, 1, 1, 28, 44, 28, 1, 1, 90, 110, 110, 90, 1, 1, 281, 581, 518, 581, 281, 1, 1, 737, 2354, 3851, 3851, 2354, 737, 1, 1, 2095, 8452, 21577, 62702, 21577, 8452, 2095, 1, 1, 6268, 35474, 124879, 649470, 649470, 124879, 35474, 6268, 1, 1

Offset

1,5

Comments

Table starts

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

.1....6.....15......28........90.........281...........737............2095

.1...15.....44.....110.......581........2354..........8452...........35474

.1...28....110.....518......3851.......21577........124879..........764482

.1...90....581....3851.....62702......649470.......6388097........74040837

.1..281...2354...21577....649470....10239175.....153675314......2926105110

.1..737...8452..124879...6388097...153675314....3710803701....113097325063

.1.2095..35474..764482..74040837..2926105110..113097325063...5908904429141

.1.6268.146560.4511480.809517928.50497979952.3060234284708.267611417815233

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) = 3*a(n-1) -2*a(n-2) +9*a(n-3) -10*a(n-4) -4*a(n-5) -4*a(n-6)

k=3: [order 10]

k=4: [order 27]

k=5: [order 67]

Example

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

Crossrefs

Sequence in context: A347672 A205133 A152238 * A086645 A168291 A154980

Adjacent sequences: A295982 A295983 A295984 * A295986 A295987 A295988

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 01 2017

Status

approved