A298230 - OEIS

A298230

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

1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 16, 5, 16, 8, 13, 50, 17, 17, 50, 13, 21, 112, 12, 195, 12, 112, 21, 34, 348, 100, 490, 490, 100, 348, 34, 55, 1028, 219, 2606, 1749, 2606, 219, 1028, 55, 89, 2796, 498, 15646, 7038, 7038, 15646, 498, 2796, 89, 144, 8216, 1999, 74688, 71212

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Table starts

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

..2....4....4.....16......50.......112........348.........1028...........2796

..3....4....5.....17......12.......100........219..........498...........1999

..5...16...17....195.....490......2606......15646........74688.........397909

..8...50...12....490....1749......7038......71212.......440402........2785299

.13..112..100...2606....7038....110320....1166270.....10448313......136604409

.21..348..219..15646...71212...1166270...25406586....353699661.....6688607300

.34.1028..498..74688..440402..10448313..353699661...7311722995...215277571718

.55.2796.1999.397909.2785299.136604409.6688607300.215277571718.11308912804354

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 18] for n>19

k=4: [order 66] for n>68

EXAMPLE

Some solutions for n=6 k=4

..0..1..1..1. .0..0..1..1. .0..1..0..1. .0..1..1..0. .0..1..0..0

..1..1..0..0. .0..0..1..1. .0..1..0..1. .0..1..1..0. .0..1..0..0

..0..1..0..0. .0..0..1..0. .1..1..0..0. .1..1..0..0. .1..1..1..0

..1..1..1..1. .0..0..1..1. .1..1..0..0. .1..1..0..0. .1..1..0..0

..1..1..0..0. .1..0..1..1. .0..0..0..1. .0..1..1..0. .0..1..0..0

..0..0..0..0. .1..0..1..1. .0..0..1..0. .0..1..1..0. .0..1..0..0

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A298148.

Sequence in context: A232451 A299451 A300089 * A298154 A299128 A299886

Adjacent sequences: A298227 A298228 A298229 * A298231 A298232 A298233

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 15 2018

STATUS

approved