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A297338
T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0 or 2 neighboring 1s.
13
2, 3, 4, 5, 8, 8, 8, 22, 21, 16, 13, 53, 96, 55, 32, 21, 134, 334, 421, 144, 64, 34, 333, 1310, 2119, 1847, 377, 128, 55, 833, 4888, 13067, 13428, 8105, 987, 256, 89, 2078, 18604, 73147, 130297, 85065, 35568, 2584, 512, 144, 5190, 70255, 427900, 1091456, 1299649
OFFSET
1,1
Table starts
...2....3......5........8.........13..........21............34..............55
...4....8.....22.......53........134.........333...........833............2078
...8...21.....96......334.......1310........4888.........18604...........70255
..16...55....421.....2119......13067.......73147........427900.........2455970
..32..144...1847....13428.....130297.....1091456.......9831967........85542000
..64..377...8105....85065....1299649....16277492.....225944546......2976461197
.128..987..35568...538819...12964224...242728633....5193690642....103574723331
.256.2584.156089..3412881..129324245..3619361855..119391166963...3603917287497
.512.6765.684994.21617001.1290083201.53967869192.2744583368968.125396477316407
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 5*a(n-1) -2*a(n-2) -3*a(n-3)
k=4: a(n) = 8*a(n-1) -10*a(n-2) -4*a(n-3) +3*a(n-4) +a(n-5)
k=5: [order 7] for n>8
k=6: [order 13] for n>14
k=7: [order 20] for n>22
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +3*a(n-2) +2*a(n-3) -a(n-5)
n=3: [order 12]
n=4: [order 31]
n=5: [order 82]
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .1..0..0..0. .0..0..1..0. .0..0..1..1. .1..0..1..0
..1..0..1..0. .0..0..1..0. .1..0..0..0. .0..1..1..0. .1..0..0..1
..0..0..1..0. .1..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..1
..0..0..0..1. .1..0..0..1. .0..0..0..1. .0..0..0..1. .1..0..0..0
..0..1..0..0. .1..0..0..1. .0..0..0..0. .1..0..0..1. .1..0..0..0
CROSSREFS
Column 1 is A000079.
Column 2 is A001906(n+1).
Row 1 is A000045(n+2).
Sequence in context: A164339 A275465 A185198 * A297457 A297694 A297637
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 28 2017
STATUS
approved

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Last modified September 19 23:07 EDT 2024. Contains 376015 sequences. (Running on oeis4.)