A198180 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4

1, 3, 9, 25, 77, 148, 395, 866, 2346, 5663, 14065, 34309, 84252, 208413, 513352, 1266410, 3117377, 7679699, 18927327, 46639092, 114949605, 283220762, 697929906, 1719783577, 4237987789, 10443340285, 25734497336, 63415169957, 156267786924

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 0's, every 4 is next to 4 0's

Column 3 of A198185

Links

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

Formula

Empirical: a(n) = a(n-1) +3*a(n-2) -a(n-3) +3*a(n-4) +14*a(n-5) -a(n-6) -13*a(n-7) -17*a(n-8) -43*a(n-9) -73*a(n-10) -111*a(n-11) -70*a(n-12) -49*a(n-13) +87*a(n-14) +274*a(n-15) +424*a(n-16) +337*a(n-17) +389*a(n-18) +202*a(n-19) +184*a(n-20) -420*a(n-21) -643*a(n-22) -580*a(n-23) -287*a(n-24) -116*a(n-25) -426*a(n-26) -5*a(n-27) +80*a(n-28) +414*a(n-29) +294*a(n-30) +24*a(n-31) -12*a(n-32) -72*a(n-33) -30*a(n-34) +4*a(n-36) +4*a(n-37)

Example

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

Crossrefs

Sequence in context: A191354 A001189 A212352 * A101786 A354647 A217995

Adjacent sequences: A198177 A198178 A198179 * A198181 A198182 A198183

Keyword

nonn

Author

R. H. Hardin Oct 21 2011

Status

approved