A317823 - OEIS

A317823

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

0, 1, 1, 1, 5, 1, 2, 16, 16, 2, 3, 50, 35, 50, 3, 5, 160, 135, 135, 160, 5, 8, 511, 356, 702, 356, 511, 8, 13, 1634, 1113, 2726, 2726, 1113, 1634, 13, 21, 5226, 3150, 11768, 8556, 11768, 3150, 5226, 21, 34, 16716, 9484, 48526, 47374, 47374, 48526, 9484, 16716, 34

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,5

COMMENTS

Table starts

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

..1.....5....16.....50.....160......511......1634.......5226.......16716

..1....16....35....135.....356.....1113......3150.......9484.......27522

..2....50...135....702....2726....11768.....48526.....203049......846901

..3...160...356...2726....8556....47374....179111.....878802.....3604079

..5...511..1113..11768...47374...296968...1458418....8231398....43470698

..8..1634..3150..48526..179111..1458418...7370716...49813114...285365386

.13..5226..9484.203049..878802..8231398..49813114..384248160..2679172247

.21.16716.27522.846901.3604079.43470698.285365386.2679172247.21424520640

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..363

FORMULA

Empirical for column k:

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

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

k=3: [order 16] for n>18

k=4: [order 37] for n>43

k=5: [order 94] for n>99

EXAMPLE

Some solutions for n=5 k=4

..0..1..1..0. .0..0..1..1. .0..1..1..0. .0..0..1..0. .0..1..1..0

..0..1..1..0. .1..1..1..0. .1..0..0..1. .1..1..1..1. .0..1..1..1

..1..1..1..0. .0..1..1..0. .0..0..0..1. .1..1..1..0. .0..1..1..0

..0..1..1..0. .0..1..0..1. .1..0..1..1. .0..1..1..0. .0..1..1..0

..0..1..0..1. .1..0..0..1. .1..0..1..0. .0..1..1..0. .0..1..1..0

CROSSREFS

Column 1 is A000045(n-1).

Sequence in context: A085608 A258339 A197080 * A318430 A318098 A318068

Adjacent sequences: A317820 A317821 A317822 * A317824 A317825 A317826

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Aug 07 2018

STATUS

approved