A318091 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 1, 5, 7, 7, 5, 1, 1, 10, 7, 47, 7, 10, 1, 1, 23, 11, 159, 159, 11, 23, 1, 1, 54, 15, 547, 493, 547, 15, 54, 1, 1, 131, 62, 1976, 1945, 1945, 1976, 62, 131, 1, 1, 321, 104, 8031, 8525, 10843, 8525, 8031, 104, 321, 1, 1, 789, 141, 32040

Offset

1,5

Comments

Table starts

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

.1...2...2.....3......5......10.......23........54........131.........321

.1...2...2.....7......7......11.......15........62........104.........141

.1...3...7....47....159.....547.....1976......8031......32040......126847

.1...5...7...159....493....1945.....8525.....37863.....161424......688404

.1..10..11...547...1945...10843....68301....432496....2725920....16794426

.1..23..15..1976...8525...68301...504606...4057433...31285292...240249513

.1..54..62..8031..37863..432496..4057433..44408035..446314981..4540720013

.1.131.104.32040.161424.2725920.31285292.446314981.5866156032.76596251675

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

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

k=3: [order 24]

Example

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

Crossrefs

Column 2 is A317809.

Sequence in context: A176809 A317815 A318423 * A301608 A285521 A187451

Adjacent sequences: A318088 A318089 A318090 * A318092 A318093 A318094

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 16 2018

Status

approved