A299052 - OEIS

A299052

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

1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 16, 11, 16, 8, 13, 50, 40, 40, 50, 13, 21, 112, 79, 455, 79, 112, 21, 34, 348, 480, 1650, 1650, 480, 348, 34, 55, 1028, 1542, 10706, 9994, 10706, 1542, 1028, 55, 89, 2796, 5317, 76068, 82340, 82340, 76068, 5317, 2796, 89, 144, 8216

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OFFSET

1,2

COMMENTS

Table starts

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

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

..3....4....11......40.......79........480.........1542...........5317

..5...16....40.....455.....1650......10706........76068.........445597

..8...50....79....1650.....9994......82340.......953445........8956381

.13..112...480...10706....82340....1731008.....29176924......456270494

.21..348..1542...76068...953445...29176924....888675946....23405238642

.34.1028..5317..445597..8956381..456270494..23405238642..1063108306477

.55.2796.22571.2902533.86708195.8295241404.693920505214.53324500523781

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A298148.

Sequence in context: A298154 A299128 A299886 * A299814 A299689 A300321

Adjacent sequences: A299049 A299050 A299051 * A299053 A299054 A299055

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 01 2018

STATUS

approved