A298554 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 18, 4, 18, 1, 1, 31, 14, 14, 31, 1, 1, 65, 16, 33, 16, 65, 1, 1, 130, 51, 74, 74, 51, 130, 1, 1, 253, 104, 226, 341, 226, 104, 253, 1, 1, 519, 262, 716, 1073, 1073, 716, 262, 519, 1, 1, 1018, 689, 2211, 3822, 4157, 3822, 2211, 689, 1018, 1

Offset

1,5

Comments

Table starts

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

.1...5...7...18....31.....65.....130......253.......519......1018.......2055

.1...7...4...14....16.....51.....104......262.......689......1784.......4767

.1..18..14...33....74....226.....716.....2211......6851.....21462......67050

.1..31..16...74...341...1073....3822....13570.....48112....176011.....641370

.1..65..51..226..1073...4157...17378....72567....310925...1345213....5838677

.1.130.104..716..3822..17378...85227...430934...2190786..11366897...58786296

.1.253.262.2211.13570..72567..430934..2586208..15726159..97403128..600617339

.1.519.689.6851.48112.310925.2190786.15726159.113602418.837791825.6166852815

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) for n>5

k=3: [order 19] for n>20

k=4: [order 72] for n>73

Example

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

Crossrefs

Column 2 is A297937.

Sequence in context: A137754 A131404 A297943 * A298727 A299561 A298382

Adjacent sequences: A298551 A298552 A298553 * A298555 A298556 A298557

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 21 2018

Status

approved