A299067 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 64, 141, 64, 3, 5, 236, 993, 993, 236, 5, 8, 888, 7330, 13765, 7330, 888, 8, 13, 3336, 54106, 196699, 196699, 54106, 3336, 13, 21, 12512, 398654, 2827609, 5491159, 2827609, 398654, 12512, 21, 34, 46928, 2937795

Offset

1,5

Comments

Table starts

..0.....1........1..........2.............3................5..................8

..1.....4.......18.........64...........236..............888...............3336

..1....18......141........993..........7330............54106.............398654

..2....64......993......13765........196699..........2827609...........40585250

..3...236.....7330.....196699.......5491159........154373324.........4331069485

..5...888....54106....2827609.....154373324.......8486867094.......465531179253

..8..3336...398654...40585250....4331069485.....465531179253.....49918355153525

.13.12512..2937795..582407760..121483918174...25530821979245...5351692051251075

.21.46928.21650600.8358259950.3407860943824.1400307860660375.573807870327017333

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

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

k=3: [order 9] for n>10

k=4: [order 22] for n>23

k=5: [order 62] for n>64

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A231950(n-1).

Sequence in context: A299142 A299373 A299937 * A299728 A299839 A265178

Adjacent sequences: A299064 A299065 A299066 * A299068 A299069 A299070

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 01 2018

Status

approved