A165386 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, and 4 in the lower right corner.

3, 40, 305, 1622, 6868, 25036, 82224, 250208, 718536, 1972132, 5220384, 13417184, 33652952, 82699012, 199729888, 475260768, 1116459752, 2593550148, 5965976992, 13605076608, 30787314104, 69191005796, 154539160288, 343241755840

Offset

2,1

Links

R. H. Hardin, Table of n, a(n) for n=2..58

Formula

Empirical: a(n) = 12*a(n-1) - 63*a(n-2) + 190*a(n-3) - 363*a(n-4) + 456*a(n-5) - 377*a(n-6) + 198*a(n-7) - 60*a(n-8) + 8*a(n-9) for n>=13.

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

G.f.: x^2*(3 + 4*x + 14*x^2 - 88*x^3 + 108*x^4 + 8*x^5 - 98*x^6 + 60*x^7 + 9*x^8 - 16*x^9 + 4*x^10) / ((1 - x)^6*(1 - 2*x)^3).

a(n) = (-314880 + 315315*2^n - (139264+79785*2^n)*n + 5*(-5248+1323*2^n)*n^2 - 3280*n^3 - 160*n^4 - 16*n^5) / 240 for n>3.

(End)

Example

Some solutions for n=4:
...1.2.2.2.......1.1.2.2.......1.2.2.2.......1.1.3.2.......1.1.2.2....
.....2.2.2.3.......2.2.2.2.......4.4.4.4.......3.3.2.2.......3.3.2.4..
.......3.3.3.4.......3.2.2.4.......3.4.4.4.......3.3.4.4.......3.4.4.4
------
...1.1.1.2.......1.1.2.2.......1.1.1.2.......1.1.1.2.......1.1.2.2....
.....1.3.2.2.......1.3.2.4.......3.3.3.3.......1.3.2.4.......3.3.3.3..
.......3.2.2.4.......3.4.4.4.......3.3.3.4.......3.4.4.4.......3.3.3.4
------
...1.2.2.2.......1.1.3.2.......1.1.2.2.......1.1.1.2.......1.1.2.2....
.....3.3.3.3.......3.3.3.3.......1.1.1.1.......2.2.2.2.......1.3.2.4..
.......3.3.4.4.......3.3.4.4.......3.3.3.4.......3.2.2.4.......3.3.4.4

Crossrefs

Sequence in context: A278379 A181395 A165395 * A293501 A002700 A220639

Adjacent sequences: A165383 A165384 A165385 * A165387 A165388 A165389

Keyword

nonn

Author

R. H. Hardin, Sep 17 2009

Status

approved