A196133 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,3,4 for x=0,1,2,3,4

1, 3, 4, 19, 31, 70, 117, 253, 538, 1169, 2401, 4896, 10179, 21291, 44754, 93367, 194747, 405806, 848007, 1772209, 3704016, 7737207, 16162351, 33766226, 70554991, 147429719, 308053298, 643669403, 1344939023, 2810299720, 5872263661

Offset

1,2

Comments

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

Column 3 of A196138

Links

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

Formula

Empirical: a(n) = a(n-1) +a(n-2) +a(n-3) +3*a(n-4) +3*a(n-5) +6*a(n-6) -5*a(n-7) -14*a(n-8) -17*a(n-9) -32*a(n-10) -25*a(n-11) -38*a(n-12) -11*a(n-13) +19*a(n-14) +39*a(n-15) +42*a(n-16) +6*a(n-17) +18*a(n-18) +20*a(n-19) +32*a(n-20) +24*a(n-21)

Example

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

Crossrefs

Sequence in context: A041703 A036253 A212113 * A330436 A025089 A041989

Adjacent sequences: A196130 A196131 A196132 * A196134 A196135 A196136

Keyword

nonn

Author

R. H. Hardin Sep 28 2011

Status

approved