A301823 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

0, 1, 0, 1, 2, 0, 2, 2, 5, 0, 3, 8, 4, 13, 0, 5, 18, 25, 8, 34, 0, 8, 50, 74, 68, 16, 89, 0, 13, 128, 278, 299, 177, 32, 233, 0, 21, 338, 968, 1351, 1197, 457, 64, 610, 0, 34, 882, 3450, 6653, 6501, 4785, 1183, 128, 1597, 0, 55, 2312, 12210, 30441, 47363, 31061, 19130, 3075

Offset

1,5

Comments

Table starts

.0....1...1....2......3.......5.........8.........13..........21............34

.0....2...2....8.....18......50.......128........338.........882..........2312

.0....5...4...25.....74.....278.......968.......3450.......12210.........43316

.0...13...8...68....299....1351......6653......30441......146175........682879

.0...34..16..177...1197....6501.....47363.....284691.....1896274......11958940

.0...89..32..457...4785...31061....333335....2626219....23877827.....205351902

.0..233..64.1183..19130..147954...2341241...24102055...298497818....3505205058

.0..610.128.3075..76499..705180..16471479..221373169..3746076847...60097022948

.0.1597.256.8018.305959.3364845.115975709.2034255683.47059520355.1030456894273

Links

R. H. Hardin, Table of n, a(n) for n = 1..416

Formula

Empirical for column k:

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

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

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

k=4: a(n) = 6*a(n-1) -13*a(n-2) +13*a(n-3) -6*a(n-4) +a(n-5)

k=5: a(n) = 8*a(n-1) -22*a(n-2) +28*a(n-3) -17*a(n-4) +4*a(n-5) for n>7

k=6: [order 16] for n>17

k=7: [order 26] for n>28

Empirical for row n:

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

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

n=3: [order 14] for n>18

n=4: [order 66] for n>72

Example

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

Crossrefs

Column 2 is A001519.

Column 3 is A000079(n-1).

Row 1 is A000045(n-1).

Row 2 is A175395(n-1).

Sequence in context: A300822 A118658 A165912 * A301999 A171936 A375372

Adjacent sequences: A301820 A301821 A301822 * A301824 A301825 A301826

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 27 2018

Status

approved