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

1,3

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513(n-2).

Row 2 is A302368.

Sequence in context: A302367 A303084 A302889 * A121439 A307448 A305350

Adjacent sequences: A303621 A303622 A303623 * A303625 A303626 A303627

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 27 2018

Status

approved