A300930 - OEIS

A300930

T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 37, 75, 37, 3, 5, 129, 508, 508, 129, 5, 8, 450, 3447, 6638, 3447, 450, 8, 13, 1568, 23404, 87561, 87561, 23404, 1568, 13, 21, 5464, 158855, 1155263, 2244335, 1155263, 158855, 5464, 21, 34, 19041, 1078231, 15238332

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

OFFSET

1,5

COMMENTS

Table starts

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

..1.....3......11.........37..........129.............450...............1568

..1....11......75........508.........3447...........23404.............158855

..2....37.....508.......6638........87561.........1155263...........15238332

..3...129....3447......87561......2244335........57594572.........1477281166

..5...450...23404....1155263.....57594572......2875574552.......143498589629

..8..1568..158855...15238332...1477281166....143498589629.....13930396115571

.13..5464.1078231..200997959..37892542998...7160975085336...1352339873296663

.21.19041.7318522.2651226860.971951600750.357354070296570.131283287305824217

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..311

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) +a(n-3) -a(n-4) for n>5

k=3: [order 8] for n>10

k=4: [order 26] for n>27

k=5: [order 64] for n>67

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A232031(n-1).

Sequence in context: A180771 A300546 A300973 * A109528 A136125 A092580

Adjacent sequences: A300927 A300928 A300929 * A300931 A300932 A300933

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 15 2018

STATUS

approved

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