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A300973 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 3, 1, 2, 11, 11, 2, 3, 37, 72, 37, 3, 5, 129, 459, 459, 129, 5, 8, 450, 2956, 5362, 2956, 450, 8, 13, 1568, 18996, 63565, 63565, 18996, 1568, 13, 21, 5464, 122043, 753471, 1396701, 753471, 122043, 5464, 21, 34, 19041, 784108, 8926774, 30679527 (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......72........459.........2956..........18996............122043

..2....37.....459.......5362........63565.........753471...........8926774

..3...129....2956......63565......1396701.......30679527.........673550354

..5...450...18996.....753471.....30679527.....1248976325.......50812633429

..8..1568..122043....8926774....673550354....50812633429.....3830408271334

.13..5464..784108..105763972..14787165263..2067233940661...288757143760689

.21.19041.5037730.1253091915.324641851765.84103618035068.21768367076769721

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..241

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 9] for n>11

k=4: [order 41] for n>42

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A232031(n-1).

Sequence in context: A301615 A180771 A300546 * A300930 A109528 A136125

Adjacent sequences:  A300970 A300971 A300972 * A300974 A300975 A300976

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 17 2018

STATUS

approved

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Last modified September 20 19:27 EDT 2021. Contains 347589 sequences. (Running on oeis4.)