A304676 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 13, 13, 1, 1, 26, 23, 23, 26, 1, 1, 49, 45, 56, 45, 49, 1, 1, 99, 131, 199, 199, 131, 99, 1, 1, 194, 337, 598, 897, 598, 337, 194, 1, 1, 387, 883, 1950, 3525, 3525, 1950, 883, 387, 1, 1, 773, 2389, 6588, 15544, 20932, 15544, 6588, 2389

Offset

1,5

Comments

Table starts

.1...1....1.....1......1.......1........1.........1...........1............1

.1...4....7....13.....26......49.......99.......194.........387..........773

.1...7...13....23.....45.....131......337.......883........2389.........6599

.1..13...23....56....199.....598.....1950......6588.......21871........72947

.1..26...45...199....897....3525....15544.....68896......310438......1387613

.1..49..131...598...3525...20932...122388....711362.....4369285.....26155072

.1..99..337..1950..15544..122388...930123...7208807....57718628....454436233

.1.194..883..6588..68896..711362..7208807..73484449...779364745...8098139458

.1.387.2389.21871.310438.4369285.57718628.779364745.11082127004.153249721883

Links

R. H. Hardin, Table of n, a(n) for n = 1..197

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) for n>5

k=3: [order 18] for n>19

k=4: [order 70] for n>71

Example

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

Crossrefs

Column 2 is A304004.

Sequence in context: A305360 A304952 A316620 * A316123 A146771 A073697

Adjacent sequences: A304673 A304674 A304675 * A304677 A304678 A304679

Keyword

nonn,tabl

Author

R. H. Hardin, May 16 2018

Status

approved