A296974 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2, 4 or 5 king-move neighboring 1s.

1, 1, 1, 1, 5, 1, 1, 11, 11, 1, 1, 21, 31, 21, 1, 1, 59, 78, 78, 59, 1, 1, 145, 295, 274, 295, 145, 1, 1, 323, 959, 1418, 1418, 959, 323, 1, 1, 793, 2958, 6573, 13543, 6573, 2958, 793, 1, 1, 1939, 9835, 29590, 101352, 101352, 29590, 9835, 1939, 1, 1, 4561, 32104, 140427

Offset

1,5

Comments

Table starts

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

.1....5....11.....21.......59........145.........323...........793

.1...11....31.....78......295........959........2958..........9835

.1...21....78....274.....1418.......6573.......29590........140427

.1...59...295...1418....13543.....101352......711867.......5662206

.1..145...959...6573...101352....1154298....12662763.....158665988

.1..323..2958..29590...711867...12662763...222799447....4440619952

.1..793..9835.140427..5662206..158665988..4440619952..143300513381

.1.1939.32104.665654.44485796.1952861999.87137716095.4520161193750

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 17]

k=4: [order 48]

Example

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

Crossrefs

Sequence in context: A181370 A119307 A296039 * A146954 A174949 A174861

Adjacent sequences: A296971 A296972 A296973 * A296975 A296976 A296977

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 22 2017

Status

approved