A305516 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 2, 2, 2, 3, 1, 5, 1, 3, 5, 8, 6, 6, 8, 5, 8, 5, 8, 10, 8, 5, 8, 13, 22, 19, 13, 13, 19, 22, 13, 21, 29, 33, 38, 62, 38, 33, 29, 21, 34, 60, 60, 73, 108, 108, 73, 60, 60, 34, 55, 121, 107, 164, 353, 343, 353, 164, 107, 121, 55, 89, 194, 204, 351, 982, 925, 925, 982

Offset

1,5

Comments

Table starts

..0..1...1...2....3....5.....8.....13.....21......34.......55........89

..1..3...2...1....8....5....22.....29.....60.....121......194.......425

..1..2...5...6....8...19....33.....60....107.....204......375.......677

..2..1...6..10...13...38....73....164....351.....749.....1719......3710

..3..8...8..13...62..108...353....982...2362....6902....17966.....48328

..5..5..19..38..108..343...925...2627...7334...20665....56990....159501

..8.22..33..73..353..925..3547..14118..43745..173690...619516...2147913

.13.29..60.164..982.2627.14118..61412.226004.1060302..4311525..17892039

.21.60.107.351.2362.7334.43745.226004.923608.4939048.23169076.107297290

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) for n>6

k=3: [order 10] for n>13

k=4: [order 14] for n>17

k=5: [order 45] for n>49

k=6: [order 91] for n>100

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297809 for n>2.

Sequence in context: A347430 A346491 A304302 * A305182 A291047 A033178

Adjacent sequences: A305513 A305514 A305515 * A305517 A305518 A305519

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 03 2018

Status

approved