A165372 Number of slanted n X 3 (i=1..n) X (j=i..3+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, and 4 in the lower right corner.

9, 40, 104, 168, 232, 296, 360, 424, 488, 552, 616, 680, 744, 808, 872, 936, 1000, 1064, 1128, 1192, 1256, 1320, 1384, 1448, 1512, 1576, 1640, 1704, 1768, 1832, 1896, 1960, 2024, 2088, 2152, 2216, 2280, 2344, 2408, 2472, 2536, 2600, 2664, 2728, 2792, 2856

Offset

2,1

Links

R. H. Hardin, Table of n, a(n) for n=2..99

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) for n>=5.

Conjectures from Colin Barker, Mar 25 2018: (Start)

G.f.: x^2*(9 + 22*x + 33*x^2) / (1 - x)^2.

a(n) = 8*(8*n-19) for n>2.

(End)

Example

Some solutions for n=6:
...1.2.2.............1.2.2.............1.1.2.............1.1.2..........
.....2.2.2.............2.2.2.............1.2.2.............1.1.1........
.......2.2.2.............2.3.3.............2.2.2.............1.1.3......
.........2.2.2.............3.3.3.............2.2.2.............3.3.3....
...........4.4.4.............3.3.3.............2.2.2.............3.3.3..
.............3.4.4.............3.3.4.............3.3.4.............3.3.4
------
...1.1.2.............1.1.2.............1.1.2.............1.1.2..........
.....1.1.1.............1.2.2.............1.1.1.............1.1.1........
.......1.1.3.............2.2.3.............1.1.1.............1.1.1......
.........3.3.3.............3.3.3.............1.1.3.............1.1.1....
...........3.3.4.............3.3.3.............3.3.4.............3.3.3..
.............3.4.4.............3.4.4.............3.4.4.............3.3.4
------
...1.1.2.............1.1.2.............1.2.2.............1.1.2..........
.....2.2.2.............2.2.3.............2.2.2.............1.1.1........
.......2.2.2.............2.3.3.............2.3.3.............1.1.1......
.........2.2.2.............3.3.3.............3.3.3.............3.3.3....
...........2.2.4.............3.3.4.............3.3.4.............3.3.4..
.............3.4.4.............3.4.4.............3.4.4.............3.4.4

Crossrefs

Sequence in context: A346336 A003354 A063164 * A264624 A287324 A006414

Adjacent sequences: A165369 A165370 A165371 * A165373 A165374 A165375

Keyword

nonn

Author

R. H. Hardin, Sep 17 2009

Status

approved