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A221683
T(n,k)=Number of 0..k arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0
10
0, 0, 2, 0, 2, 4, 0, 2, 5, 8, 0, 2, 5, 14, 16, 0, 2, 5, 20, 40, 32, 0, 2, 5, 26, 68, 113, 64, 0, 2, 5, 32, 100, 241, 320, 128, 0, 2, 5, 38, 133, 418, 844, 906, 256, 0, 2, 5, 44, 166, 636, 1692, 2966, 2565, 512, 0, 2, 5, 50, 199, 891, 2856, 6932, 10413, 7262, 1024, 0, 2, 5, 56, 232
OFFSET
1,3
COMMENTS
Table starts
....0.....0......0.......0.......0........0........0........0........0
....2.....2......2.......2.......2........2........2........2........2
....4.....5......5.......5.......5........5........5........5........5
....8....14.....20......26......32.......38.......44.......50.......56
...16....40.....68.....100.....133......166......199......232......265
...32...113....241.....418.....636......891.....1182.....1509.....1872
...64...320....844....1692....2856.....4326.....6102.....8184....10572
..128...906...2966....6932...13169....21985....33710....48674....67202
..256..2565..10413...28288...60120...109567...180382...276317...401105
..512..7262..36568..115604..275632...551027...980490..1606710..2476200
.1024.20560.128408..472188.1261451..2759757..5289023..9228224.15012528
.2048.58209.450913.1929012.5777107.13846871.28634131.53334307.91896348
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) for n>2
k=2: a(n) = 2*a(n-1) +2*a(n-2) +a(n-3)
k=3: a(n) = 3*a(n-1) +2*a(n-2) -a(n-3) +a(n-4)
k=4: a(n) = 3*a(n-1) +4*a(n-2) +6*a(n-4) +4*a(n-5) +4*a(n-6)
k=5: a(n) = 4*a(n-1) +3*a(n-2) -6*a(n-3) +19*a(n-4) +5*a(n-5) +a(n-6)
k=6: a(n) = 4*a(n-1) +5*a(n-2) -7*a(n-3) +33*a(n-4) +17*a(n-5) +24*a(n-6) -5*a(n-7) +2*a(n-8)
k=7: a(n) = 5*a(n-1) +3*a(n-2) -16*a(n-3) +65*a(n-4) -14*a(n-5) +23*a(n-6) +2*a(n-7) +8*a(n-8)
Empirical for row n:
n=1: a(n) = 0
n=2: a(n) = 2
n=3: a(n) = 5 for n>1
n=4: a(n) = 6*n + 2
n=5: a(n) = 33*n - 32 for n>3
n=6: a(n) = 18*n^2 + 57*n - 99 for n>4
n=7: a(n) = 153*n^2 - 213*n + 96 for n>3
EXAMPLE
Some solutions for n=6 k=4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....0....1....1....1....1....0....0....0....0....1....0....0....0....0....1
..2....0....0....0....4....1....4....4....0....2....1....1....1....0....0....2
..1....2....3....1....3....2....3....3....1....3....3....1....2....0....1....3
..1....1....4....2....2....1....2....3....4....2....3....1....1....0....1....0
..0....2....4....2....1....0....3....4....4....2....4....2....1....1....2....1
CROSSREFS
Row 4 is A016933
Sequence in context: A117946 A061930 A209691 * A332760 A199335 A141660
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Jan 22 2013
STATUS
approved