login
A302309
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
13
1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 13, 10, 16, 13, 31, 26, 33, 21, 32, 21, 113, 48, 66, 58, 42, 64, 34, 363, 121, 194, 153, 153, 86, 128, 55, 813, 275, 663, 445, 380, 336, 179, 256, 89, 1751, 600, 2048, 1595, 1271, 1090, 937, 370, 512, 144, 5001, 1296, 5790, 4772, 5715
OFFSET
1,2
COMMENTS
Table starts
...1...2....3....5.....8.....13......21.......34........55.........89
...2...3...11...21....31....113.....363......813......1751.......5001
...4...6...13...26....48....121.....275......600......1296.......2998
...8..10...33...66...194....663....2048.....5790.....17761......58980
..16..21...58..153...445...1595....4772....15249.....49634.....166329
..32..42..153..380..1271...5715...18992....70289....276303....1198933
..64..86..336.1090..3915..18990...76642...360898...1695748....9408402
.128.179..937.3120.12420..73663..364922..2150420..13123505...95790405
.256.370.2449.9130.42897.312122.1991487.15392485.124691962.1235540899
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 13] for n>16
k=4: [order 60] for n>61
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
n=3: [order 15] for n>16
n=4: [order 61] for n>64
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..1. .0..0..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..0. .0..1..0..1. .0..1..1..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .0..0..0..0. .1..0..0..1. .1..1..0..0
..0..1..0..1. .0..1..0..1. .1..1..1..0. .1..0..1..0. .0..1..0..1
..0..1..1..1. .0..1..1..1. .1..0..1..0. .1..0..1..0. .0..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Sequence in context: A302427 A303197 A059185 * A303040 A302877 A303525
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 05 2018
STATUS
approved