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A301608 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero. 7
1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 1, 6, 8, 8, 6, 1, 1, 10, 13, 25, 13, 10, 1, 1, 21, 26, 65, 65, 26, 21, 1, 1, 42, 55, 226, 330, 226, 55, 42, 1, 1, 86, 154, 755, 1297, 1297, 755, 154, 86, 1, 1, 179, 356, 2539, 6393, 8888, 6393, 2539, 356, 179, 1, 1, 370, 884, 8794, 30904 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Table starts
.1..1...1....1......1.......1........1..........1...........1............1
.1..2...2....3......6......10.......21.........42..........86..........179
.1..2...2....8.....13......26.......55........154.........356..........884
.1..3...8...25.....65.....226......755.......2539........8794........30539
.1..6..13...65....330....1297.....6393......30904......154041.......764894
.1.10..26..226...1297....8888....60841.....421168.....2940940.....20639456
.1.21..55..755...6393...60841...591585....5880829....58383932....585233819
.1.42.154.2539..30904..421168..5880829...83224304..1180228568..16849867573
.1.86.356.8794.154041.2940940.58383932.1180228568.23865691820.485485211198
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 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 18]
k=4: [order 66]
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..1. .0..1..0..1. .0..0..0..0. .0..0..1..1
..0..0..1..1. .1..1..0..1. .1..0..1..0. .0..1..0..0. .0..0..1..1
..1..1..0..0. .1..0..1..1. .0..1..0..1. .0..0..1..0. .0..0..1..1
..1..1..0..0. .1..1..1..0. .1..0..1..0. .1..0..0..0. .0..1..0..0
..1..1..0..0. .1..1..0..1. .0..1..0..1. .0..1..0..0. .0..0..0..0
CROSSREFS
Column 2 is A240513(n-2).
Sequence in context: A317815 A318423 A318091 * A285521 A187451 A134542
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 24 2018
STATUS
approved

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Last modified April 14 04:54 EDT 2024. Contains 371655 sequences. (Running on oeis4.)