A302889 - OEIS

A302889

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

1, 1, 2, 1, 2, 4, 1, 12, 2, 8, 1, 20, 37, 3, 16, 1, 72, 53, 141, 6, 32, 1, 168, 197, 238, 569, 10, 64, 1, 496, 818, 2278, 1102, 2262, 21, 128, 1, 1296, 2548, 12782, 20937, 5570, 8968, 42, 256, 1, 3616, 10926, 98458, 200186, 206332, 28594, 35667, 86, 512, 1, 9760, 42671

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Table starts

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

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

...4..2.....37.....53.......197.........818..........2548...........10926

...8..3....141....238......2278.......12782.........98458..........714934

..16..6....569...1102.....20937......200186.......2727690........37626360

..32.10...2262...5570....206332.....3452246......89290791......2247650354

..64.21...8968..28594...2059835....60501563....2899297652....133518102376

.128.42..35667.149206..20622709..1073161270...94799190457...7977498513759

.256.86.141839.788373.206851726.19073141368.3098646840396.476377988322833

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: [order 10]

k=4: [order 35] for n>37

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 51] for n>54

EXAMPLE

Some solutions for n=5 k=4

..0..1..1..0. .0..1..1..1. .0..1..1..0. .0..0..0..0. .0..1..1..0

..1..1..1..0. .1..1..1..0. .0..1..1..0. .1..0..0..1. .0..1..1..1

..0..1..1..0. .0..1..1..0. .0..1..1..1. .1..0..0..1. .0..1..1..1

..0..1..1..0. .0..1..1..1. .1..1..1..0. .0..0..0..0. .1..1..1..0

..0..1..1..1. .0..1..1..0. .0..1..1..1. .0..0..0..1. .1..1..1..0

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A240513(n-2).

Row 2 is A302368.

Sequence in context: A303242 A302367 A303084 * A303624 A121439 A307448

Adjacent sequences: A302886 A302887 A302888 * A302890 A302891 A302892

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 15 2018

STATUS

approved