A296128 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2 or 5 king-move neighboring 1s.

1, 1, 1, 1, 5, 1, 1, 9, 9, 1, 1, 13, 18, 13, 1, 1, 33, 30, 30, 33, 1, 1, 69, 107, 74, 107, 69, 1, 1, 121, 265, 287, 287, 265, 121, 1, 1, 253, 553, 841, 2098, 841, 553, 253, 1, 1, 529, 1505, 2463, 9344, 9344, 2463, 1505, 529, 1, 1, 1013, 3852, 7953, 35733, 54286, 35733, 7953

Offset

1,5

Comments

Table starts

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

.1...5....9....13.....33.......69.......121........253.........529.........1013

.1...9...18....30....107......265.......553.......1505........3852.........8922

.1..13...30....74....287......841......2463.......7953.......24428........74660

.1..33..107...287...2098.....9344.....35733.....182881......859151......3752449

.1..69..265...841...9344....54286....263489....1867837....11720327.....67180741

.1.121..553..2463..35733...263489...1810441...16855693...138016847...1087543621

.1.253.1505..7953.182881..1867837..16855693..227074899..2614792001..28292082465

.1.529.3852.24428.859151.11720327.138016847.2614792001.41069612676.599261543598

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

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

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

k=4: [order 9]

k=5: [order 39]

Example

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

Crossrefs

Column 2 is A089977(n+1).

Column 3 is A183444.

Sequence in context: A153108 A157174 A183450 * A131061 A157169 A081578

Adjacent sequences: A296125 A296126 A296127 * A296129 A296130 A296131

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 05 2017

Status

approved