A299398 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 61, 113, 61, 3, 5, 216, 628, 628, 216, 5, 8, 793, 3641, 5663, 3641, 793, 8, 13, 2907, 21375, 51588, 51588, 21375, 2907, 13, 21, 10622, 124972, 479767, 755157, 479767, 124972, 10622, 21, 34, 38809, 730509, 4442111, 11246136

Offset

1,5

Comments

Table starts

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

..1.....4......17........61.........216...........793............2907

..1....17.....113.......628........3641.........21375..........124972

..2....61.....628......5663.......51588........479767.........4442111

..3...216....3641.....51588......755157......11246136.......166665723

..5...793...21375....479767....11246136.....268557163......6375889022

..8..2907..124972...4442111...166665723....6375889022....242153450727

.13.10622..730509..41117169..2469920505..151409151272...9202140590865

.21.38809.4271331.380674402.36615834468.3597323154240.349916213368020

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 13] for n>15

k=4: [order 48] for n>50

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297917.

Column 3 is A298332.

Column 4 is A298333.

Sequence in context: A297923 A298547 A298337 * A299228 A300040 A206359

Adjacent sequences: A299395 A299396 A299397 * A299399 A299400 A299401

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 09 2018

Status

approved