A303624 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 1, 2, 1, 2, 4, 1, 12, 2, 8, 1, 20, 38, 3, 16, 1, 72, 68, 148, 6, 32, 1, 168, 362, 325, 616, 10, 64, 1, 496, 1283, 3591, 1870, 2520, 21, 128, 1, 1296, 5411, 19467, 37910, 10741, 10288, 42, 256, 1, 3616, 22516, 160807, 350410, 398859, 62207, 42100, 86, 512, 1, 9760

Offset: 1

Author

R. H. Hardin, Apr 27 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

...2..2.....12......20........72.........168...........496.............1296

...4..2.....38......68.......362........1283..........5411............22516

...8..3....148.....325......3591.......19467........160807..........1173612

..16..6....616....1870.....37910......350410.......5249045.........70522741

..32.10...2520...10741....398859.....6446485.....179884814.......4470005178

..64.21..10288...62207...4288358...122517773....6323564388.....290118140045

.128.42..42100..363485..46208517..2348299355..224091914399...18955122420980

.256.86.172268.2135551.499581127.45211204167.7966090548780.1240883902751147

Examples

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

Links

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513(n-2).

Row 2 is A302368.

Formula

Empirical for column k:

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

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

k=3: a(n) = 5*a(n-1) -5*a(n-2) +8*a(n-3) -12*a(n-4) +4*a(n-5) -4*a(n-6) for n>8

k=4: [order 22] for n>24

k=5: [order 62] for n>65

Empirical for row n:

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

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

n=3: [order 16] for n>17

n=4: [order 43] for n>44