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A165378
Number of slanted n X 4 (i=1..n) X (j=i..4+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, 4 in the lower right corner, and with no element having more than 2 neighbors with the same value.
1
33, 94, 158, 243, 346, 467, 606, 763, 938, 1131, 1342, 1571, 1818, 2083, 2366, 2667, 2986, 3323, 3678, 4051, 4442, 4851, 5278, 5723, 6186, 6667, 7166, 7683, 8218, 8771, 9342, 9931, 10538, 11163, 11806, 12467, 13146, 13843, 14558, 15291, 16042, 16811
OFFSET
2,1
LINKS
FORMULA
Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>=7.
Conjectures from Colin Barker, Mar 26 2018: (Start)
G.f.: x^2*(33 - 5*x - 25*x^2 + 18*x^3 - 3*x^4) / (1 - x)^3.
a(n) = 9*n^2 + 4*n - 2 for n>3.
(End)
EXAMPLE
Some solutions for n=4:
...1.1.2.2.........1.1.2.2.........1.1.1.2.........1.1.2.2......
.....1.1.3.4.........1.1.4.4.........3.3.2.2.........1.1.2.2....
.......1.3.4.4.........1.3.4.4.........3.3.2.2.........3.3.4.4..
.........3.3.4.4.........3.3.4.4.........3.3.3.4.........3.3.4.4
------
...1.1.2.2.........1.1.2.2.........1.2.2.2.........1.1.2.2......
.....1.3.2.2.........3.3.2.2.........3.3.2.2.........1.3.2.2....
.......3.3.4.4.........3.3.4.4.........3.3.2.2.........3.3.2.3..
.........3.3.4.4.........3.3.4.4.........3.3.3.4.........3.3.3.4
------
...1.1.2.2.........1.1.2.2.........1.1.2.2.........1.3.2.2......
.....1.1.1.4.........1.1.2.2.........1.2.4.4.........3.3.2.2....
.......3.3.4.4.........1.3.4.4.........2.2.4.4.........3.3.2.3..
.........3.3.4.4.........3.3.4.4.........3.3.4.4.........3.3.3.4
CROSSREFS
Sequence in context: A350220 A305221 A316799 * A098938 A098923 A044220
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 17 2009
STATUS
approved