A165382 Number of slanted n X 5 (i=1..n) X (j=i..5+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.

105, 1382, 6412, 18900, 40058, 70658, 110364, 159322, 217548, 284834, 361612, 447194, 542556, 646402, 760380, 882458, 1015084, 1155362, 1306668, 1465114, 1635132, 1811714, 2000476, 2195162, 2402700, 2615458, 2841804, 3072602, 3317788

Offset

2,1

Links

R. H. Hardin, Table of n, a(n) for n=2..41

Formula

Empirical: a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>=13.

Empirical g.f.: x^2*(105 + 1382*x + 6097*x^2 + 14754*x^3 + 21137*x^4 + 18104*x^5 + 9321*x^6 + 2666*x^7 + 218*x^8 - 58*x^9 + 2*x^10) / ((1 - x)^3*(1 + x)^3). - Colin Barker, Mar 26 2018

Example

Some solutions for n=3:
...1.2.2.2.2.......1.2.2.2.2.......1.1.1.2.2.......1.1.1.2.2....
.....3.3.2.3.3.......2.3.2.4.4.......3.3.3.3.4.......3.3.2.4.4..
.......3.3.3.3.4.......3.3.3.4.4.......3.3.3.4.4.......3.3.3.4.4
------
...1.1.2.2.2.......1.1.3.3.2.......1.1.1.1.2.......1.1.2.2.2....
.....3.3.2.2.2.......1.3.3.2.2.......2.2.2.2.4.......3.3.4.4.4..
.......3.3.3.3.4.......3.3.2.4.4.......3.2.4.4.4.......3.3.3.4.4
------
...1.1.1.1.2.......1.1.1.1.2.......1.2.2.2.2.......1.1.3.3.2....
.....1.2.2.2.2.......3.3.3.2.2.......3.3.3.2.2.......3.3.2.2.3..
.......3.3.4.4.4.......3.3.4.4.4.......3.2.2.2.4.......3.3.3.3.4

Crossrefs

Sequence in context: A266105 A058844 A297800 * A051015 A221449 A076377

Adjacent sequences: A165379 A165380 A165381 * A165383 A165384 A165385

Keyword

nonn

Author

R. H. Hardin, Sep 17 2009

Status

approved