A316733 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 5, 13, 1, 1, 26, 9, 9, 26, 1, 1, 49, 15, 11, 15, 49, 1, 1, 99, 17, 20, 20, 17, 99, 1, 1, 194, 40, 17, 55, 17, 40, 194, 1, 1, 387, 73, 25, 201, 201, 25, 73, 387, 1, 1, 773, 87, 70, 337, 137, 337, 70, 87, 773, 1, 1, 1538, 219, 67, 1359, 42, 42, 1359

Offset

1,5

Comments

Starts to differ from A305047 at (n=7, k=7). - R. H. Hardin, Aug 04 2018

Table starts

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

.1...4..7.13...26...49...99.....194.....387.....773......1538.......3081

.1...7..5..9...15...17...40......73......87.....219.......433........583

.1..13..9.11...20...17...25......70......67.....101.......292........325

.1..26.15.20...55..201..337....1359....5918...13840.....50917.....214418

.1..49.17.17..201..137...42....5165....6357....5846....188507.....395242

.1..99.40.25..337...42..275....6652....3399....8908....160954.....203593

.1.194.73.70.1359.5165.6652..274113.1476693.3813273..72793968..506693539

.1.387.87.67.5918.6357.3399.1476693.2083319.2387357.399292140.1133955731

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)

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

k=3: [order 11] for n>13

k=4: [order 9] for n>13

Example

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

Crossrefs

Column 2 is A304004.

Column 3 is A305042.

Column 4 is A305043.

Column 5 is A305044.

Column 6 is A305045.

Sequence in context: A146986 A304141 A305047 * A304010 A305360 A304952

Adjacent sequences: A316730 A316731 A316732 * A316734 A316735 A316736

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 11 2018

Status

approved