A165374 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, and 4 in the lower right corner.

105, 1622, 11960, 63740, 272548, 993780, 3239860, 9743508, 27593908, 74632788, 194702068, 493466004, 1221540916, 2965389012, 7081701748, 16678011924, 38810916532, 89383135572, 203992087540, 461842419348, 1038214750516

Offset

2,1

Links

R. H. Hardin, Table of n, a(n) for n=2..48

Formula

Empirical: a(n) = 8*a(n-1) - 25*a(n-2) + 38*a(n-3) - 28*a(n-4) + 8*a(n-5) for n>=11.

Empirical g.f.: x^2*(105 + 782*x + 1609*x^2 + 4620*x^3 + 2932*x^4 - 3008*x^5 + 3104*x^6 + 1344*x^7 + 128*x^8) / ((1 - x)^2*(1 - 2*x)^3). - Colin Barker, Mar 26 2018

Example

Some solutions for n=3:
...1.2.2.2.2.......1.1.1.2.2.......1.1.2.2.2.......1.1.1.2.2....
.....3.3.3.2.2.......1.1.1.2.4.......1.3.3.2.2.......1.1.1.2.2..
.......3.2.2.2.4.......3.3.2.4.4.......3.3.4.4.4.......3.1.2.4.4
------
...1.1.2.2.2.......1.1.1.2.2.......1.1.1.1.2.......1.1.2.2.2....
.....1.1.1.1.1.......1.2.2.2.2.......1.1.1.2.2.......1.1.2.2.2..
.......3.3.3.3.4.......3.3.2.4.4.......3.3.3.4.4.......3.4.4.4.4
------
...1.1.2.2.2.......1.1.1.3.2.......1.1.2.2.2.......1.1.2.2.2....
.....1.2.3.2.4.......3.3.3.2.2.......2.2.2.4.4.......2.2.2.4.4..
.......3.3.3.4.4.......3.2.2.4.4.......3.4.4.4.4.......3.2.2.4.4

Crossrefs

Sequence in context: A051015 A221449 A076377 * A024198 A027788 A112497

Adjacent sequences: A165371 A165372 A165373 * A165375 A165376 A165377

Keyword

nonn

Author

R. H. Hardin, Sep 17 2009

Status

approved