A296963 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2, 3 or 5 king-move neighboring 1s.

1, 1, 1, 1, 6, 1, 1, 16, 16, 1, 1, 31, 60, 31, 1, 1, 96, 177, 177, 96, 1, 1, 301, 869, 910, 869, 301, 1, 1, 801, 3994, 6506, 6506, 3994, 801, 1, 1, 2261, 16348, 44519, 88469, 44519, 16348, 2261, 1, 1, 6746, 71669, 289576, 1064451, 1064451, 289576, 71669, 6746, 1, 1

Offset

1,5

Comments

Table starts

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

.1....6.....16.......31.........96..........301............801............2261

.1...16.....60......177........869.........3994..........16348...........71669

.1...31....177......910.......6506........44519.........289576.........1933227

.1...96....869.....6506......88469......1064451.......11592086.......134880572

.1..301...3994....44519....1064451.....21225209......374855869......7251402774

.1..801..16348...289576...11592086....374855869....10777843410....340260590831

.1.2261..71669..1933227..134880572...7251402774...340260590831..17890820040132

.1.6746.320252.12967823.1582121415.141096153092.10761797803245.941238613911895

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) = 4*a(n-1) -5*a(n-2) +11*a(n-3) -18*a(n-4) +4*a(n-5)

k=3: [order 21]

k=4: [order 51]

Example

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

Crossrefs

Sequence in context: A109001 A203005 A357156 * A176560 A152602 A119726

Adjacent sequences: A296960 A296961 A296962 * A296964 A296965 A296966

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 22 2017

Status

approved