A318350 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 3, 5, 4, 4, 5, 8, 7, 6, 7, 8, 13, 11, 13, 13, 11, 13, 21, 18, 21, 14, 21, 18, 21, 34, 30, 41, 29, 29, 41, 30, 34, 55, 49, 71, 55, 62, 55, 71, 49, 55, 89, 81, 130, 106, 136, 136, 106, 130, 81, 89, 144, 134, 237, 220, 279, 345, 279, 220, 237, 134, 144, 233, 221, 439

Offset

1,2

Comments

Table starts

..1..2...3...5....8...13....21.....34.....55......89.....144......233.......377

..2..3...4...7...11...18....30.....49.....81.....134.....221......365.......603

..3..4...6..13...21...41....71....130....237.....439.....802.....1483......2734

..5..7..13..14...29...55...106....220....432.....885....1788.....3642......7416

..8.11..21..29...62..136...279....624...1344....2941....6444....14202.....31437

.13.18..41..55..136..345...842...2167...5544...14244...36572....94381....243153

.21.30..71.106..279..842..2429...7451..22996...70762..218768...677035...2090867

.34.49.130.220..624.2167..7451..27666.102454..375150.1393359..5163458..19078931

.55.81.237.432.1344.5544.22996.102454.463096.2057916.9235301.41554051.186399590

Links

R. H. Hardin, Table of n, a(n) for n = 1..510

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +2*a(n-3) -a(n-6)

k=3: [order 19] for n>25

k=4: [order 37] for n>45

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A317767.

Sequence in context: A301662 A317773 A318082 * A127332 A087826 A131624

Adjacent sequences: A318347 A318348 A318349 * A318351 A318352 A318353

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 24 2018

Status

approved