A299937 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 64, 130, 64, 3, 5, 236, 902, 902, 236, 5, 8, 888, 6243, 11212, 6243, 888, 8, 13, 3336, 43375, 144072, 144072, 43375, 3336, 13, 21, 12512, 300901, 1858165, 3441754, 1858165, 300901, 12512, 21, 34, 46928, 2088188

Offset

1,5

Comments

Table starts

..0.....1........1..........2.............3...............5.................8

..1.....4.......18.........64...........236.............888..............3336

..1....18......130........902..........6243...........43375............300901

..2....64......902......11212........144072.........1858165..........23924290

..3...236.....6243.....144072.......3441754........82403876........1969988474

..5...888....43375....1858165......82403876......3664429516......162678451993

..8..3336...300901...23924290....1969988474....162678451993....13409569414628

.13.12512..2088188..308062375...47097894761...7222553677769..1105467648686714

.21.46928.14490885.3966828615.1126027901118.320673103163046.91135851756212849

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) = 4*a(n-1) -2*a(n-2) +4*a(n-3) for n>4

k=3: [order 10] for n>11

k=4: [order 33] for n>34

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A231950(n-1).

Sequence in context: A298280 A299142 A299373 * A299067 A299728 A299839

Adjacent sequences: A299934 A299935 A299936 * A299938 A299939 A299940

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 22 2018

Status

approved