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A301400 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 4, 3, 4, 0, 0, 9, 13, 13, 9, 0, 0, 19, 44, 78, 44, 19, 0, 0, 41, 156, 446, 446, 156, 41, 0, 0, 88, 554, 2619, 4857, 2619, 554, 88, 0, 0, 189, 1963, 15538, 49325, 49325, 15538, 1963, 189, 0, 0, 406, 6964, 92338, 521514, 885003, 521514 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,8
COMMENTS
Table starts
.0...0....0......0........0..........0............0..............0
.0...1....2......4........9.........19...........41.............88
.0...2....3.....13.......44........156..........554...........1963
.0...4...13.....78......446.......2619........15538..........92338
.0...9...44....446.....4857......49325.......521514........5457161
.0..19..156...2619....49325.....885003.....16325745......299552320
.0..41..554..15538...521514...16325745....528025038....16971131642
.0..88.1963..92338..5457161..299552320..16971131642...956047339302
.0.189.6964.549096.57311190.5507220522.546618326745.53967719265287
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3)
k=3: [order 15]
k=4: [order 45]
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..0
..0..0..1..1. .0..0..1..1. .0..1..1..1. .0..0..1..1. .0..0..0..0
..0..0..1..0. .0..0..1..0. .1..1..0..0. .0..0..0..0. .1..1..0..0
..0..1..0..0. .0..0..0..0. .1..0..0..1. .0..1..0..0. .1..0..1..1
..1..1..0..0. .0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..1..1
CROSSREFS
Column 2 is A078039(n-2).
Sequence in context: A300465 A300646 A300776 * A134315 A268584 A119332
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 20 2018
STATUS
approved

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Last modified May 22 20:45 EDT 2024. Contains 372758 sequences. (Running on oeis4.)