A304149 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 14, 14, 2, 3, 33, 18, 33, 3, 5, 70, 25, 25, 70, 5, 8, 157, 113, 61, 113, 157, 8, 13, 346, 238, 157, 157, 238, 346, 13, 21, 769, 359, 117, 1198, 117, 359, 769, 21, 34, 1710, 1309, 244, 3484, 3484, 244, 1309, 1710, 34, 55, 3813, 3091, 936, 5336, 13152

Offset

1,5

Comments

Table starts

..0....1....1...2.....3......5......8.......13........21........34.........55

..1....7...14..33....70....157....346......769......1710......3813.......8514

..1...14...18..25...113....238....359.....1309......3091......5173......15475

..2...33...25..61...157....117....244......936.......733......1513.......5788

..3...70..113.157..1198...3484...5336....24401.....90422....181207.....546435

..5..157..238.117..3484..13152..12582...139840....774023...1302357....5969791

..8..346..359.244..5336..12582...6492...218516....748819....579549....8291908

.13..769.1309.936.24401.139840.218516..1429403..12033436..34502082..116115677

.21.1710.3091.733.90422.774023.748819.12033436.180869894.471888374.2046852451

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

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

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

k=3: [order 14] for n>16

k=4: [order 17] for n>22

k=5: [order 93] for n>96

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A354639 A273984 A119506 * A305489 A305089 A316740

Adjacent sequences: A304146 A304147 A304148 * A304150 A304151 A304152

Keyword

nonn,tabl

Author

R. H. Hardin, May 07 2018

Status

approved