A164749 Number of n X 3 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.

8, 108, 730, 3576, 14414, 50928, 163722, 490496, 1391862, 3784168, 9940066, 25384568, 63327166, 154906432, 372640634, 883653200, 2069574918, 4794856504, 11003621330, 25040248584, 56557140046, 126889144656, 282971569898

Offset

2,1

Links

R. H. Hardin, Table of n, a(n) for n = 2..52

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 >= 11.

Empirical g.f.: 2*x^2*(4 + 6*x - 31*x^2 + 50*x^3 - 62*x^4 + 52*x^5 - 7*x^6 - 12*x^7 + 4*x^8) / ((1 - x)^6*(1 - 2*x)^3). - Colin Barker, Mar 25 2018

Example

Some solutions for n=4:
  1 1 2   1 2 2   1 1 2   1 1 2   1 2 2   1 1 2   1 1 2   1 1 2   1 2 2
  1 1 1   1 4 4   1 4 4   3 2 2   2 2 2   3 3 2   3 1 2   1 1 1   1 1 4
  3 4 4   4 4 4   4 4 4   3 2 4   4 4 2   3 3 2   3 3 4   3 1 1   1 1 4
  3 3 4   3 3 4   3 3 4   3 4 4   3 4 4   3 4 4   3 3 4   3 4 4   3 4 4
------
  1 2 2   1 1 2   1 4 2   1 2 2   1 2 2   1 2 2   1 2 2   1 1 2   1 2 2
  1 2 2   1 2 2   1 4 4   1 3 2   1 1 1   3 3 3   1 2 2   3 4 2   1 1 2
  2 2 4   1 2 2   1 4 4   3 3 3   3 3 3   3 3 4   3 3 2   3 4 4   3 1 4
  3 3 4   3 4 4   3 3 4   3 4 4   3 3 4   3 4 4   3 3 4   3 3 4   3 1 4

Crossrefs

Sequence in context: A246498 A119936 A276296 * A264487 A048543 A300468

Adjacent sequences: A164746 A164747 A164748 * A164750 A164751 A164752

Keyword

nonn

Author

R. H. Hardin, Aug 24 2009

Status

approved