A299814 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 16, 12, 16, 8, 13, 50, 43, 43, 50, 13, 21, 112, 91, 476, 91, 112, 21, 34, 348, 519, 1739, 1739, 519, 348, 34, 55, 1028, 1721, 11312, 11460, 11312, 1721, 1028, 55, 89, 2796, 5886, 80892, 91721, 91721, 80892, 5886, 2796, 89, 144, 8216

Offset

1,2

Comments

Table starts

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

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

..3....4....12......43.......91........519.........1721...........5886

..5...16....43.....476.....1739......11312........80892.........470799

..8...50....91....1739....11460......91721......1087487.......10193140

.13..112...519...11312....91721....1881856.....32361748......503025918

.21..348..1721...80892..1087487...32361748...1009387819....26528688317

.34.1028..5886..470799.10193140..503025918..26528688317..1201130067486

.55.2796.24858.3083661.99383076.9210499641.792668582776.60813283508109

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 17] for n>18

k=4: [order 55] for n>58

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A298148.

Sequence in context: A299128 A299886 A299052 * A299689 A300321 A026254

Adjacent sequences: A299811 A299812 A299813 * A299815 A299816 A299817

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 19 2018

Status

approved