A298389 - OEIS

A298389

T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5 or 6 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 52, 56, 52, 3, 5, 174, 223, 223, 174, 5, 8, 604, 849, 996, 849, 604, 8, 13, 2048, 3387, 5180, 5180, 3387, 2048, 13, 21, 6948, 13075, 26926, 49850, 26926, 13075, 6948, 21, 34, 23652, 51006, 135226, 384118, 384118, 135226, 51006

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OFFSET

1,5

COMMENTS

Table starts

..0.....1......1.......2.........3..........5............8............13

..1.....4.....18......52.......174........604.........2048..........6948

..1....18.....56.....223.......849.......3387........13075.........51006

..2....52....223.....996......5180......26926.......135226........690918

..3...174....849....5180.....49850.....384118......2837337......23616114

..5...604...3387...26926....384118....3935913.....38706835.....445387553

..8..2048..13075..135226...2837337...38706835....509195874....8032883165

.13..6948..51006..690918..23616114..445387553...8032883165..190487814086

.21.23652.199243.3547086.189866553.4869394793.118750882425.4054091346048

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) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6

k=3: [order 20] for n>21

k=4: [order 69] for n>71

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A297945.

Sequence in context: A206359 A297951 A298560 * A299307 A298770 A299567

Adjacent sequences: A298386 A298387 A298388 * A298390 A298391 A298392

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 18 2018

STATUS

approved