A165395 Number of slanted 3 X n (i=1..3) X (j=i..n+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 3 neighbors with the same value.

3, 40, 285, 1382, 5472, 18912, 59472, 174568, 486352, 1300936, 3368528, 8494280, 20955536, 50756232, 121033104, 284778120, 662333776, 1524945352, 3479910352, 7878810440, 17713527824, 39574755848, 87916721424, 194311523592

Offset

2,1

Links

R. H. Hardin, Table of n, a(n) for n=2..56

Formula

Empirical: a(n) = 10*a(n-1) - 42*a(n-2) + 96*a(n-3) - 129*a(n-4) + 102*a(n-5) - 44*a(n-6) + 8*a(n-7) for n>=12.

Empirical g.f.: x^2*(3 + 10*x + 11*x^2 - 76*x^3 + 169*x^4 - 270*x^5 + 321*x^6 - 216*x^7 + 88*x^8 - 8*x^9) / ((1 - x)^4*(1 - 2*x)^3). - Colin Barker, Mar 26 2018

Example

Some solutions for n=4:
...1.1.2.2.......1.3.3.2.......1.1.2.2.......1.1.2.2.......1.1.1.2....
.....3.3.3.3.......3.3.2.2.......1.1.1.1.......1.3.2.2.......1.3.3.3..
.......3.3.3.4.......3.3.4.4.......3.3.4.4.......3.3.3.4.......3.3.3.4
------
...1.1.3.2.......1.1.2.2.......1.3.2.2.......1.1.3.2.......1.1.1.2....
.....3.3.2.3.......1.2.2.3.......3.3.2.4.......3.3.2.2.......1.1.1.1..
.......3.3.3.4.......3.3.3.4.......3.3.4.4.......3.2.2.4.......3.4.4.4
------
...1.1.1.2.......1.1.1.2.......1.1.3.2.......1.1.2.2.......1.1.2.2....
.....1.3.2.3.......1.3.2.4.......3.3.2.2.......1.2.3.4.......3.3.3.4..
.......3.3.3.4.......3.2.4.4.......3.3.3.4.......3.3.4.4.......3.3.4.4

Crossrefs

Sequence in context: A013292 A278379 A181395 * A165386 A293501 A002700

Adjacent sequences: A165392 A165393 A165394 * A165396 A165397 A165398

Keyword

nonn

Author

R. H. Hardin, Sep 17 2009

Status

approved