A305360 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 13, 13, 13, 1, 1, 26, 21, 21, 26, 1, 1, 49, 27, 26, 27, 49, 1, 1, 99, 53, 64, 64, 53, 99, 1, 1, 194, 99, 115, 137, 115, 99, 194, 1, 1, 387, 197, 211, 271, 271, 211, 197, 387, 1, 1, 773, 371, 439, 656, 538, 656, 439, 371, 773, 1, 1, 1538, 713, 870

Offset

1,5

Comments

Table starts

.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

.1...7..13..21...27...53....99...197....371.....713....1365.....2645.....5105

.1..13..21..26...64..115...211...439....870....1725....3513.....7141....14372

.1..26..27..64..137..271...656..1414...3251....7823...17334....40796....93604

.1..49..53.115..271..538..1476..3001...8018...19631...49142...121150...301994

.1..99..99.211..656.1476..4429.11281..31062...84750..233266...652271..1795948

.1.194.197.439.1414.3001.11281.33136..96562..302341..927289..2823816..8720038

.1.387.371.870.3251.8018.31062.96562.321576.1100993.3656995.12269156.41412932

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 16] for n>17

k=4: [order 67] for n>70

Example

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

Crossrefs

Column 2 is A304004.

Column 3 is A304005.

Column 4 is A304006.

Sequence in context: A305047 A316733 A304010 * A304952 A316620 A304676

Adjacent sequences: A305357 A305358 A305359 * A305361 A305362 A305363

Keyword

nonn,tabl

Author

R. H. Hardin, May 31 2018

Status

approved