A304141 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3 or 6 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, 16, 20, 20, 16, 99, 1, 1, 194, 33, 17, 39, 17, 33, 194, 1, 1, 387, 57, 25, 83, 83, 25, 57, 387, 1, 1, 773, 62, 62, 135, 39, 135, 62, 62, 773, 1, 1, 1538, 133, 59, 356, 34, 34, 356, 59, 133

Offset

1,5

Comments

Table starts

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

.1...4..7.13..26..49..99...194...387...773...1538....3081....6147....12298

.1...7..5..9..15..16..33....57....62...133....231.....256.....549......953

.1..13..9.11..20..17..25....62....59....93....220.....237.....381......830

.1..26.15.20..39..83.135...356...967..1769...4507...12371...26399....63179

.1..49.16.17..83..39..34...749...257...102...8887....2522.....603...104361

.1..99.33.25.135..34..48...785....96...164...5607.....688....1198....43126

.1.194.57.62.356.749.785.11067.31406.35953.290885.1165507.1782306..8735753

.1.387.62.59.967.257..96.31406..8405...577.975952..406351...56557.28610665

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

k=3: [order 8] for n>10

k=4: a(n) = 2*a(n-1) +2*a(n-3) -6*a(n-4) +3*a(n-6) for n>10

k=5: [order 91] for n>96

Example

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

Crossrefs

Column 2 is A304004.

Sequence in context: A047671 A081577 A146986 * A305047 A316733 A304010

Adjacent sequences: A304138 A304139 A304140 * A304142 A304143 A304144

Keyword

nonn,tabl

Author

R. H. Hardin, May 07 2018

Status

approved