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A302150 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero. 11
1, 1, 2, 1, 1, 4, 1, 2, 1, 8, 1, 2, 4, 1, 16, 1, 3, 5, 10, 1, 32, 1, 6, 11, 17, 28, 1, 64, 1, 10, 34, 56, 65, 84, 1, 128, 1, 21, 88, 255, 289, 257, 260, 1, 256, 1, 42, 271, 1038, 2005, 1529, 1025, 816, 1, 512, 1, 86, 798, 4771, 12212, 15999, 8152, 4097, 2576, 1, 1024, 1, 179 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Table starts

...1.1....1.....1......1.......1.........1..........1............1

...2.1....2.....2......3.......6........10.........21...........42

...4.1....4.....5.....11......34........88........271..........798

...8.1...10....17.....56.....255......1038.......4771........21866

..16.1...28....65....289....2005.....12212......83092.......578398

..32.1...84...257...1529...15999....145150....1482725.....15902462

..64.1..260..1025...8152..128319...1728734...26544210....439103633

.128.1..816..4097..43676.1030709..20614702..476725579..12181287002

.256.1.2576.16385.234707.8283143.245896061.8575073202.338788296901

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..363

FORMULA

Empirical for column k:

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

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

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

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

k=5: [order 12]

k=6: [order 7] for n>9

k=7: [order 51] for n>54

Empirical for row n:

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

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

n=3: [order 25] for n>27

n=4: [order 85] for n>89

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 4 is A052539(n-2).

Row 2 is A240513(n-3).

Sequence in context: A208482 A199856 A301906 * A193554 A131350 A131087

Adjacent sequences:  A302147 A302148 A302149 * A302151 A302152 A302153

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 02 2018

STATUS

approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)