A320364 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 4, 2, 0, 0, 5, 13, 13, 5, 0, 0, 16, 60, 97, 60, 16, 0, 0, 45, 258, 657, 657, 258, 45, 0, 0, 123, 1111, 4563, 7902, 4563, 1111, 123, 0, 0, 340, 4836, 32371, 91711, 91711, 32371, 4836, 340, 0, 0, 946, 21007, 228784, 1076811, 1752652, 1076811

Offset

1,12

Comments

Table starts

.0...0.....0.......0.........0...........0.............0..............0

.0...1.....1.......2.........5..........16............45............123

.0...1.....4......13........60.........258..........1111...........4836

.0...2....13......97.......657........4563.........32371.........228784

.0...5....60.....657......7902.......91711.......1076811.......12633183

.0..16...258....4563.....91711.....1752652......33825987......653183942

.0..45..1111...32371...1076811....33825987....1076542482....34268936133

.0.123..4836..228784..12633183...653183942...34268936133..1799446075386

.0.340.21007.1612859.148082443.12600432002.1089237599640.94302533172340

Links

R. H. Hardin, Table of n, a(n) for n = 1..198

Formula

Empirical for column k:

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

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

k=3: [order 18] for n>20

k=4: [order 56] for n>58

Example

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

Crossrefs

Column 2 is A317890.

Sequence in context: A058672 A278215 A317896 * A318222 A209466 A277659

Adjacent sequences: A320361 A320362 A320363 * A320365 A320366 A320367

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 11 2018

Status

approved