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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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 17 2009
STATUS
approved