A299689 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 16, 15, 16, 8, 13, 50, 54, 54, 50, 13, 21, 112, 156, 648, 156, 112, 21, 34, 348, 854, 2850, 2850, 854, 348, 34, 55, 1028, 3226, 20882, 23116, 20882, 3226, 1028, 55, 89, 2796, 13013, 159324, 251922, 251922, 159324, 13013, 2796, 89

Offset

1,2

Comments

Table starts

..1....2.....3.......5.........8..........13............21..............34

..2....4.....4......16........50.........112...........348............1028

..3....4....15......54.......156.........854..........3226...........13013

..5...16....54.....648......2850.......20882........159324.........1041908

..8...50...156....2850.....23116......251922.......3247879........36816394

.13..112...854...20882....251922.....5740433.....120453362......2322958629

.21..348..3226..159324...3247879...120453362....4582634341....154482346317

.34.1028.13013.1041908..36816394..2322958629..154482346317...9172624830461

.55.2796.56318.7459468.431156277.49439157520.5662974500151.587385690244582

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) +a(n-2)

k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

k=3: [order 15] for n>17

k=4: [order 44] for n>46

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A298148.

Sequence in context: A299886 A299052 A299814 * A300321 A026254 A091525

Adjacent sequences: A299686 A299687 A299688 * A299690 A299691 A299692

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 16 2018

Status

approved