A300888 - OEIS

A300888

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

1, 2, 2, 3, 3, 3, 5, 2, 2, 5, 8, 3, 4, 3, 8, 13, 6, 8, 8, 6, 13, 21, 6, 17, 40, 17, 6, 21, 34, 11, 57, 121, 121, 57, 11, 34, 55, 26, 148, 465, 808, 465, 148, 26, 55, 89, 43, 356, 1822, 5309, 5309, 1822, 356, 43, 89, 144, 82, 864, 7045, 31867, 47487, 31867, 7045, 864, 82, 144

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OFFSET

1,2

COMMENTS

Table starts

..1..2...3.....5.......8.......13.........21..........34............55

..2..3...2.....3.......6........6.........11..........26............43

..3..2...4.....8......17.......57........148.........356...........864

..5..3...8....40.....121......465.......1822........7045.........27552

..8..6..17...121.....808.....5309......31867......195259.......1186702

.13..6..57...465....5309....47487.....437276.....3964190......36386491

.21.11.148..1822...31867...437276....6236246....88486037....1253495751

.34.26.356..7045..195259..3964190...88486037..1923849671...41503841765

.55.43.864.27552.1186702.36386491.1253495751.41503841765.1369615742014

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..199

FORMULA

Empirical for column k:

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

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

k=3: [order 21] for n>25

k=4: [order 96] for n>100

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A300500.

Sequence in context: A324019 A275378 A300506 * A300944 A301498 A136132

Adjacent sequences: A300885 A300886 A300887 * A300889 A300890 A300891

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 14 2018

STATUS

approved