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A303314 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12
1, 2, 2, 3, 3, 4, 5, 3, 4, 8, 8, 5, 12, 6, 16, 13, 7, 17, 11, 9, 32, 21, 13, 24, 36, 19, 14, 64, 34, 23, 67, 50, 74, 34, 22, 128, 55, 37, 158, 128, 139, 165, 53, 35, 256, 89, 63, 298, 439, 410, 349, 361, 83, 56, 512, 144, 109, 595, 1085, 1799, 1221, 853, 783, 136, 90, 1024, 233 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
...1..2...3....5....8....13.....21......34.......55........89........144
...2..3...3....5....7....13.....23......37.......63.......109........183
...4..4..12...17...24....67....158.....298......595......1337.......2863
...8..6..11...36...50...128....439....1085.....2431......6452......17455
..16..9..19...74..139...410...1799....5907....16494.....53290.....184915
..32.14..34..165..349..1221...7096...30280...102683....403872....1783894
..64.22..53..361..853..3453..26184..148313...618149...2955145...16591424
.128.35..83..783.2180.10223.100128..746323..3851318..22515378..159560449
.256.56.136.1710.5525.30247.387892.3784002.23967605.171306353.1539204838
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) -a(n-3)
k=3: a(n) = a(n-1) +a(n-3) +a(n-4) for n>7
k=4: a(n) = a(n-1) +a(n-2) +3*a(n-3) +2*a(n-4) -a(n-5) -2*a(n-6) -a(n-7) for n>10
k=5: a(n) = a(n-1) +9*a(n-3) +2*a(n-4) +4*a(n-5) -10*a(n-6) -6*a(n-7) +4*a(n-9) for n>12
k=6: [order 8] for n>11
k=7: [order 20] for n>23
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +2*a(n-3) for n>5
n=3: a(n) = a(n-1) +3*a(n-3) +4*a(n-4) for n>7
n=4: a(n) = a(n-1) +a(n-2) +5*a(n-3) +9*a(n-4) -3*a(n-5) -7*a(n-6) -2*a(n-7) for n>11
n=5: [order 12] for n>16
n=6: [order 23] for n>28
n=7: [order 46] for n>51
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..0. .0..1..1..1. .0..0..0..1. .0..1..0..0. .0..1..0..1
..0..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..1..1. .0..1..1..1
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .0..0..0..1. .0..1..0..1. .0..1..0..1
..0..0..0..1. .0..0..0..1. .1..1..0..1. .0..1..0..1. .0..1..0..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A001611(n+1).
Row 1 is A000045(n+1).
Row 2 is A003229(n-1) for n>2.
Sequence in context: A119446 A302680 A302515 * A349122 A076918 A162620
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 21 2018
STATUS
approved

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Last modified March 28 13:35 EDT 2024. Contains 371254 sequences. (Running on oeis4.)