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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 14 2018
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)