A196680 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,1,2,3 for x=0,1,2,3,4

4, 20, 58, 292, 1235, 5186, 22461, 96256, 413032, 1780597, 7673860, 33017186, 142219489, 612618957, 2638803566, 11367909928, 48973948677, 210982341958, 908945163931, 3915948771137, 16870934284560, 72684969189462

Offset

1,1

Comments

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

Column 3 of A196685

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +4*a(n-2) -6*a(n-3) +10*a(n-4) -60*a(n-5) -160*a(n-6) -634*a(n-7) -1583*a(n-8) +297*a(n-9) +2182*a(n-10) +9602*a(n-11) +42284*a(n-12) +39581*a(n-13) +18230*a(n-14) +15645*a(n-15) -60179*a(n-16) -28875*a(n-17) +1218*a(n-18) -23566*a(n-19) +46466*a(n-20) -35766*a(n-21) -50232*a(n-22) -41220*a(n-23) -33792*a(n-24) +26772*a(n-25) +17644*a(n-26) +18228*a(n-27) +6120*a(n-28) +4281*a(n-29) +3612*a(n-30) +772*a(n-31) -1467*a(n-32) -815*a(n-33) -304*a(n-34) -271*a(n-35) -35*a(n-36) +19*a(n-37) +3*a(n-38)

Example

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

Crossrefs

Sequence in context: A066970 A196295 A196213 * A033488 A018211 A135507

Adjacent sequences: A196677 A196678 A196679 * A196681 A196682 A196683

Keyword

nonn

Author

R. H. Hardin Oct 05 2011

Status

approved