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A318214 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 3, 1, 2, 6, 6, 2, 3, 10, 4, 10, 3, 5, 21, 21, 21, 21, 5, 8, 46, 47, 69, 47, 46, 8, 13, 102, 125, 245, 245, 125, 102, 13, 21, 220, 329, 698, 1042, 698, 329, 220, 21, 34, 491, 842, 2321, 4794, 4794, 2321, 842, 491, 34, 55, 1077, 2254, 7528, 20502, 28010, 20502 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

..0...1....1.....2......3.......5........8........13..........21...........34

..1...3....6....10.....21......46......102.......220.........491.........1077

..1...6....4....21.....47.....125......329.......842........2254.........5893

..2..10...21....69....245.....698.....2321......7528.......24531........80826

..3..21...47...245...1042....4794....20502.....93848......413543......1866198

..5..46..125...698...4794...28010...155972....921216.....5383356.....31881211

..8.102..329..2321..20502..155972..1122773...8679924....65844976....507320695

.13.220..842..7528..93848..921216..8679924..93034400...949653285...9710509636

.21.491.2254.24531.413543.5383356.65844976.949653285.12949799902.174194567097

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..220

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = a(n-1) +4*a(n-2) -2*a(n-3) -2*a(n-4) +a(n-5) -4*a(n-6) +4*a(n-7) -a(n-8)

k=3: [order 32] for n>33

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A317857.

Sequence in context: A102035 A055179 A317863 * A318552 A183289 A183253

Adjacent sequences:  A318211 A318212 A318213 * A318215 A318216 A318217

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Aug 21 2018

STATUS

approved

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Last modified May 9 19:28 EDT 2021. Contains 343746 sequences. (Running on oeis4.)