A165392 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 2 neighbors with the same value.

1, 9, 33, 65, 101, 146, 199, 260, 329, 406, 491, 584, 685, 794, 911, 1036, 1169, 1310, 1459, 1616, 1781, 1954, 2135, 2324, 2521, 2726, 2939, 3160, 3389, 3626, 3871, 4124, 4385, 4654, 4931, 5216, 5509, 5810, 6119, 6436, 6761, 7094, 7435, 7784, 8141, 8506

Offset

2,2

Comments

Same recurrence for A165381.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>=9.

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

G.f.: x^2*(1 + 6*x + 9*x^2 - 8*x^3 - 4*x^4 + 5*x^5 - x^6) / (1 - x)^3.

a(n) = 4*n^2 - 7*n - 1 for n>5.

(End)

Example

Some solutions for n=9:
...1.1.1.1.1.2.2.2.2.....1.1.1.1.1.1.2.2.2.....1.1.1.1.1.2.2.2.2..
.....3.3.3.1.1.1.1.2.4.....3.3.3.2.2.2.4.4.4.....3.3.3.1.1.4.4.4.4
------
...1.1.1.1.1.1.2.2.2.....1.3.3.3.3.3.3.2.2.....1.1.1.2.2.2.2.2.2..
.....3.3.3.3.4.4.4.4.4.....3.4.4.4.4.4.4.4.4.....3.3.3.3.3.4.4.4.4
------
...1.1.1.1.1.2.2.2.2.....1.1.1.1.1.1.1.1.2.....1.1.1.1.1.1.3.2.2..
.....3.3.3.2.2.4.4.4.4.....3.3.3.3.3.3.1.2.4.....3.3.3.3.3.3.2.2.4

Crossrefs

Cf. A165381.

Sequence in context: A161430 A175369 A046895 * A145923 A092562 A103602

Adjacent sequences: A165389 A165390 A165391 * A165393 A165394 A165395

Keyword

nonn

Author

R. H. Hardin, Sep 17 2009

Status

approved