A305340 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 12, 9, 16, 32, 22, 26, 26, 22, 32, 64, 45, 62, 81, 62, 45, 64, 128, 101, 166, 267, 267, 166, 101, 128, 256, 218, 431, 938, 1185, 938, 431, 218, 256, 512, 477, 1091, 3186, 5296, 5296, 3186, 1091, 477, 512, 1024, 1041, 2812, 10840

Offset

1,2

Comments

Table starts

...1...2....4.....8.....16......32.......64.......128.........256..........512

...2...4....5.....9.....22......45......101.......218.........477.........1041

...4...5...12....26.....62.....166......431......1091........2812.........7268

...8...9...26....81....267.....938.....3186.....10840.......37115.......127093

..16..22...62...267...1185....5296....23348....103641......460756......2046399

..32..45..166...938...5296...30826...176673...1020555.....5903993.....34127533

..64.101..431..3186..23348..176673..1321695...9959836....75112075....566241938

.128.218.1091.10840.103641.1020555..9959836..98008416...964336401...9486731570

.256.477.2812.37115.460756.5903993.75112075.964336401.12373093291.158745150050

Links

R. H. Hardin, Table of n, a(n) for n = 1..391

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +3*a(n-2) +3*a(n-3) +2*a(n-4) -3*a(n-5) -8*a(n-6) -4*a(n-7) for n>8

k=4: [order 15] for n>19

k=5: [order 32] for n>34

k=6: [order 62] for n>66

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A052962 for n>2.

Sequence in context: A230014 A319414 A303961 * A304604 A316420 A304926

Adjacent sequences: A305337 A305338 A305339 * A305341 A305342 A305343

Keyword

nonn,tabl

Author

R. H. Hardin, May 30 2018

Status

approved