A318068 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 5, 1, 2, 18, 18, 2, 3, 67, 98, 67, 3, 5, 249, 649, 649, 249, 5, 8, 925, 4003, 7170, 4003, 925, 8, 13, 3437, 25106, 76927, 76927, 25106, 3437, 13, 21, 12770, 156846, 829137, 1405892, 829137, 156846, 12770, 21, 34, 47447, 980960, 8929364, 25994502

Offset

1,5

Comments

Table starts

..0.....1.......1..........2............3..............5................8

..1.....5......18.........67..........249............925.............3437

..1....18......98........649.........4003..........25106...........156846

..2....67.....649.......7170........76927.........829137..........8929364

..3...249....4003......76927......1405892.......25994502........479322719

..5...925...25106.....829137.....25994502......824452611......26085599617

..8..3437..156846....8929364....479322719....26085599617....1415459855958

.13.12770..980960...96178466...8844178475...825766558967...76853282341918

.21.47447.6133497.1035919809.163160290206.26137612655323.4172233315256556

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

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

k=3: [order 11] for n>12

k=4: [order 39]

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A317823 A318430 A318098 * A165449 A019114 A201526

Adjacent sequences: A318065 A318066 A318067 * A318069 A318070 A318071

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 15 2018

Status

approved