A317815 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2 or 3 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, 4, 4, 5, 1, 1, 10, 5, 7, 5, 10, 1, 1, 23, 8, 34, 34, 8, 23, 1, 1, 54, 9, 56, 38, 56, 9, 54, 1, 1, 131, 28, 77, 94, 94, 77, 28, 131, 1, 1, 321, 44, 228, 230, 142, 230, 228, 44, 321, 1, 1, 789, 60, 551, 552, 434, 434, 552, 551, 60, 789, 1

Offset

1,5

Comments

Table starts

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

.1...2..2...3....5...10....23....54....131....321.....789....1943.....4788

.1...2..2...4....5....8.....9....28.....44.....60.....118.....256......409

.1...3..4...7...34...56....77...228....551...1300....3171....6929....16038

.1...5..5..34...38...94...230...552...1397...3674....9184...23878....60774

.1..10..8..56...94..142...434..1071...2279...6087...15953...40210...104488

.1..23..9..77..230..434..1575..4232..10738..32307...97258..284543...844473

.1..54.28.228..552.1071..4232.13712..35752.110093..343180.1067786..3331483

.1.131.44.551.1397.2279.10738.35752.112854.377515.1253484.4165180.14146154

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

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 17] for n>19

k=4: [order 48] for n>52

Example

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

Crossrefs

Sequence in context: A326038 A122632 A176809 * A318423 A318091 A301608

Adjacent sequences: A317812 A317813 A317814 * A317816 A317817 A317818

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 07 2018

Status

approved