A317863 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 6, 6, 2, 3, 10, 4, 10, 3, 5, 21, 19, 19, 21, 5, 8, 46, 32, 56, 32, 46, 8, 13, 102, 72, 155, 155, 72, 102, 13, 21, 220, 164, 313, 350, 313, 164, 220, 21, 34, 491, 331, 851, 1001, 1001, 851, 331, 491, 34, 55, 1077, 790, 2147, 2616, 3315, 2616, 2147, 790

Offset

1,5

Comments

Table starts

..0...1...1....2.....3.....5......8......13......21.......34........55

..1...3...6...10....21....46....102.....220.....491.....1077......2393

..1...6...4...19....32....72....164.....331.....790.....1700......3879

..2..10..19...56...155...313....851....2147....5513....14288.....37168

..3..21..32..155...350..1001...2616....7926...21882....65134....190018

..5..46..72..313..1001..3315...9045...28091...87900...278545....886735

..8.102.164..851..2616..9045..33238..116271..405766..1489264...5416535

.13.220.331.2147..7926.28091.116271..517734.1946626..8076505..33329441

.21.491.790.5513.21882.87900.405766.1946626.8875636.40432932.186507496

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +4*a(n-2) -2*a(n-3) -2*a(n-4) +a(n-5) -4*a(n-6) +4*a(n-7) -a(n-8)

k=3: [order 26] for n>32

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A102035 A055179 A360634 * A318214 A318552 A183289

Adjacent sequences: A317860 A317861 A317862 * A317864 A317865 A317866

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 09 2018

Status

approved