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A295120 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s. 7
1, 2, 2, 3, 5, 3, 4, 9, 9, 4, 6, 20, 26, 20, 6, 9, 41, 77, 77, 41, 9, 13, 85, 226, 326, 226, 85, 13, 19, 178, 665, 1373, 1373, 665, 178, 19, 28, 369, 1960, 5793, 8257, 5793, 1960, 369, 28, 41, 769, 5769, 24347, 49302, 49302, 24347, 5769, 769, 41, 60, 1600, 16983, 102398 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
..1...2.....3......4........6.........9.........13...........19............28
..2...5.....9.....20.......41........85........178..........369...........769
..3...9....26.....77......226.......665.......1960.........5769.........16983
..4..20....77....326.....1373......5793......24347.......102398........431050
..6..41...226...1373.....8257.....49302.....295083......1768323......10586331
..9..85...665...5793....49302....420519....3590821.....30650456.....261518933
.13.178..1960..24347...295083...3590821...43655680....530696748....6452840307
.19.369..5769.102398..1768323..30650456..530696748...9196006628..159316011413
.28.769.16983.431050.10586331.261518933.6452840307.159316011413.3931962260999
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-3)
k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-4)
k=3: [order 10]
k=4: [order 14]
k=5: [order 40]
k=6: [order 78]
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..0. .0..1..0..0. .0..0..0..0. .1..0..0..0. .1..1..0..0
..0..1..0..0. .1..1..1..0. .0..1..1..0. .1..0..1..1. .0..0..0..0
..1..0..0..0. .0..1..0..0. .0..0..0..1. .0..0..0..0. .0..0..1..0
..1..0..0..1. .1..0..1..0. .0..0..0..1. .0..0..0..0. .0..0..1..0
..0..0..0..1. .1..0..1..0. .0..1..1..0. .1..1..0..0. .0..0..0..0
CROSSREFS
Column 1 is A000930(n+1).
Column 2 is A105309(n+1).
Sequence in context: A225622 A196436 A197199 * A196957 A124727 A210565
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 15 2017
STATUS
approved

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Last modified June 23 10:38 EDT 2024. Contains 373643 sequences. (Running on oeis4.)