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A302367 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 13
1, 1, 2, 1, 2, 4, 1, 12, 2, 8, 1, 20, 31, 3, 16, 1, 72, 20, 109, 6, 32, 1, 168, 154, 77, 397, 10, 64, 1, 496, 284, 918, 209, 1430, 21, 128, 1, 1296, 1109, 3125, 6580, 774, 5110, 42, 256, 1, 3616, 3472, 21831, 26458, 49293, 3143, 18395, 86, 512, 1, 9760, 12763, 125193 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Table starts
...1..1.....1.....1........1.........1...........1.............1
...2..2....12....20.......72.......168.........496..........1296
...4..2....31....20......154.......284........1109..........3472
...8..3...109....77......918......3125.......21831........125193
..16..6...397...209.....6580.....26458......405340.......3462040
..32.10..1430...774....49293....330505.....9361759.....134269527
..64.21..5110..3143...367512...3858625...188443738....4558781926
.128.42.18395.13556..2856621..48375470..4174802035..169314399506
.256.86.66203.60280.22185382.608124211.91302504318.6186362081201
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 12]
k=4: [order 50] for n>53
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 2*a(n-1) +4*a(n-2) -4*a(n-3) -4*a(n-4)
n=3: [order 16] for n>18
n=4: [order 63] for n>66
EXAMPLE
Some solutions for n=5 k=4
..0..1..1..0. .0..1..1..0. .0..0..1..0. .0..0..1..1. .0..1..1..0
..1..1..1..1. .0..1..1..0. .0..0..1..0. .0..0..1..1. .1..1..1..1
..0..1..0..0. .1..1..1..1. .0..1..1..1. .0..1..1..0. .1..1..0..0
..0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..1. .1..1..0..0
..0..1..0..0. .0..0..0..1. .1..0..0..1. .0..0..1..1. .1..1..0..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240513(n-2).
Sequence in context: A302212 A302460 A303242 * A303084 A302889 A303624
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 06 2018
STATUS
approved

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Last modified July 17 14:36 EDT 2024. Contains 374377 sequences. (Running on oeis4.)