A298087 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 0, 2, 0, 0, 11, 3, 3, 11, 0, 0, 13, 1, 10, 1, 13, 0, 0, 34, 7, 28, 28, 7, 34, 0, 0, 65, 18, 76, 154, 76, 18, 65, 0, 0, 123, 52, 213, 520, 520, 213, 52, 123, 0, 0, 266, 144, 645, 1574, 2767, 1574, 645, 144, 266, 0, 0, 499, 405, 1852, 7204, 11202

Offset

1,8

Comments

Table starts

.0...0...0....0.....0......0.......0........0.........0..........0...........0

.0...1...3....2....11.....13......34.......65.......123........266.........499

.0...3...0....3.....1......7......18.......52.......144........405........1124

.0...2...3...10....28.....76.....213......645......1852.......5642.......17016

.0..11...1...28...154....520....1574.....7204.....28790.....105055......437163

.0..13...7...76...520...2767...11202....66148....385999....2040394....11280309

.0..34..18..213..1574..11202...65218...479206...3481050...24695892...177272585

.0..65..52..645..7204..66148..479206..4883926..46039875..420410890..3947485108

.0.123.144.1852.28790.385999.3481050.46039875.603770100.7267200831.90210295443

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

Formula

Empirical for column k:

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

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

k=3: [order 16] for n>17

k=4: [order 57] for n>58

Example

Some solutions for n=7 k=4
..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..0
..0..1..0..1. .0..1..0..1. .1..0..1..1. .0..1..0..1. .0..1..1..0
..1..1..0..1. .1..0..0..1. .1..1..1..1. .1..0..1..0. .1..0..1..0
..0..0..1..1. .0..1..0..1. .0..0..1..1. .1..0..1..0. .1..0..1..0
..0..0..0..0. .0..1..1..1. .0..1..0..0. .1..0..1..0. .1..0..1..0
..0..0..1..0. .1..0..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1
..0..0..1..1. .1..1..0..0. .0..0..1..1. .0..0..0..0. .0..0..1..1

Crossrefs

Column 2 is A297870.

Sequence in context: A325010 A297876 A298139 * A298259 A298930 A298895

Adjacent sequences: A298084 A298085 A298086 * A298088 A298089 A298090

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 12 2018

Status

approved