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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. 1
3, 40, 285, 1382, 5472, 18912, 59472, 174568, 486352, 1300936, 3368528, 8494280, 20955536, 50756232, 121033104, 284778120, 662333776, 1524945352, 3479910352, 7878810440, 17713527824, 39574755848, 87916721424, 194311523592 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 21 00:36 EDT 2022. Contains 353886 sequences. (Running on oeis4.)