A197800 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,1,0,1 for x=0,1,2,3,4.

2, 16, 102, 596, 3713, 22742, 139212, 853186, 5231300, 32071177, 196597389, 1205159672, 7387795113, 45288409942, 277625447176, 1701887549750, 10432835696321, 63954921521562, 392053737458675, 2403351095713061

Offset

1,1

Comments

Every 0 is next to 0 4's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 1's.

Column 3 of A197805.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 3*a(n-1) +6*a(n-2) +55*a(n-3) +93*a(n-4) +335*a(n-5) +452*a(n-6) +139*a(n-7) -1793*a(n-8) -3659*a(n-9) -6365*a(n-10) -7501*a(n-11) -3080*a(n-12) +14194*a(n-13) +48711*a(n-14) +46798*a(n-15) +16724*a(n-16) -51146*a(n-17) -68258*a(n-18) -58699*a(n-19) -12222*a(n-20) +5431*a(n-21) +7158*a(n-22) +52233*a(n-23) +9954*a(n-24) +5396*a(n-25) +905*a(n-26) -3014*a(n-27) +1824*a(n-28) +1787*a(n-29) -198*a(n-30) -430*a(n-31) -72*a(n-32).

Example

Some solutions for n=4:
..0..0..0....0..3..0....1..2..1....0..3..0....0..0..0....2..1..0....1..2..0
..0..0..3....3..0..3....1..0..0....0..0..1....0..0..1....1..0..3....0..1..0
..1..2..0....0..0..0....2..1..0....1..0..2....1..0..2....0..0..0....1..0..0
..0..1..0....0..0..0....0..0..0....2..1..1....2..1..1....0..3..0....2..1..0

Crossrefs

Sequence in context: A197202 A361814 A032260 * A209645 A207062 A207398

Adjacent sequences: A197797 A197798 A197799 * A197801 A197802 A197803

Keyword

nonn

Author

R. H. Hardin, Oct 18 2011

Status

approved