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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 17 2009
STATUS
approved

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Last modified July 20 20:50 EDT 2024. Contains 374459 sequences. (Running on oeis4.)