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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 8 17:55 EDT 2022. Contains 356016 sequences. (Running on oeis4.)