A165394 Number of slanted 2 X n (i=1..2) 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.

1, 9, 37, 105, 241, 481, 869, 1457, 2305, 3481, 5061, 7129, 9777, 13105, 17221, 22241, 28289, 35497, 44005, 53961, 65521, 78849, 94117, 111505, 131201, 153401, 178309, 206137, 237105, 271441, 309381, 351169, 397057, 447305, 502181, 561961, 626929

Offset

2,2

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>=7.

Conjectures from Colin Barker, Mar 26 2018: (Start)

G.f.: x^2*(1 + x)*(1 + 3*x - x^2 + x^3) / (1 - x)^5.

a(n) = (15 - 20*n + 11*n^2 - 4*n^3 + n^4) / 3.

(End)

Example

Some solutions for n=6:
...1.1.2.2.2.2.....1.3.3.3.2.2.....1.1.1.1.1.2.....1.1.3.2.2.2..
.....3.3.4.4.4.4.....3.3.3.2.4.4.....3.3.2.2.2.4.....3.3.2.2.2.4
------
...1.1.1.2.2.2.....1.1.1.3.3.2.....1.3.3.3.2.2.....1.1.1.2.2.2..
.....3.1.1.4.4.4.....3.3.3.3.2.4.....3.3.3.3.2.4.....3.1.2.2.2.4
------
...1.1.1.1.4.2.....1.1.2.2.2.2.....1.3.2.2.2.2.....1.3.2.2.2.2..
.....3.3.4.4.4.4.....3.2.2.4.4.4.....3.3.3.3.4.4.....3.3.3.2.2.4

Crossrefs

Sequence in context: A304290 A244245 A288116 * A213570 A271908 A257448

Adjacent sequences: A165391 A165392 A165393 * A165395 A165396 A165397

Keyword

nonn

Author

R. H. Hardin, Sep 17 2009

Status

approved