A296725 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 2 or 4 king-move neighboring 1s.

2, 3, 3, 5, 9, 5, 8, 21, 21, 8, 13, 57, 69, 57, 13, 21, 153, 258, 258, 153, 21, 34, 393, 963, 1463, 963, 393, 34, 55, 1041, 3493, 8315, 8315, 3493, 1041, 55, 89, 2745, 12860, 44668, 72533, 44668, 12860, 2745, 89, 144, 7185, 47305, 246923, 579857, 579857, 246923

Offset

1,1

Comments

Table starts

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

..3....9.....21......57.......153.........393.........1041...........2745

..5...21.....69.....258.......963........3493........12860..........47305

..8...57....258....1463......8315.......44668.......246923........1364492

.13..153....963....8315.....72533......579857......4846823.......40521141

.21..393...3493...44668....579857.....6829945.....84312938.....1042553987

.34.1041..12860..246923...4846823....84312938...1554755519....28740762011

.55.2745..47305.1364492..40521141..1042553987..28740762011...795154816254

.89.7185.173498.7488185.334815607.12735280455.523224064059.21598350633016

Links

R. H. Hardin, Table of n, a(n) for n = 1..238

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +2*a(n-2) +6*a(n-3)

k=3: [order 10]

k=4: [order 18]

k=5: [order 45]

Example

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

Crossrefs

Column 1 is A000045(n+2).

Sequence in context: A317644 A194000 A295781 * A296588 A065460 A241741

Adjacent sequences: A296722 A296723 A296724 * A296726 A296727 A296728

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 19 2017

Status

approved