A235012 Number of (n+1) X (3+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

264, 488, 936, 1912, 4008, 8760, 19560, 44952, 105128, 250744, 605928, 1483288, 3663912, 9124728, 22858344, 57552408, 145440680, 368673400, 936669672, 2384161816, 6076987176, 15506905464, 39603020136, 101209873944, 258785240744

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 4*a(n-1) + 4*a(n-2) - 30*a(n-3) + 7*a(n-4) + 74*a(n-5) - 46*a(n-6) - 60*a(n-7) + 48*a(n-8).

Empirical g.f.: 8*x*(33 - 71*x - 259*x^2 + 517*x^3 + 676*x^4 - 1224*x^5 - 584*x^6 + 944*x^7) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)*(1 - 3*x^2)*(1 - x - 4*x^2)). - Colin Barker, Oct 16 2018

Example

Some solutions for n=4:
  4 2 0 1     3 2 1 2     0 1 0 2     2 3 4 3     0 4 0 4
  0 1 2 0     2 4 0 4     4 2 4 3     0 4 2 4     1 2 1 2
  4 2 0 1     4 3 2 3     0 1 0 2     1 2 3 2     2 0 2 0
  0 1 2 0     2 4 0 4     4 2 4 3     2 0 4 0     1 2 1 2
  4 2 0 1     3 2 1 2     2 3 2 4     0 1 2 1     2 0 2 0

Crossrefs

Column 3 of A235017.

Sequence in context: A050240 A105683 A160971 * A211713 A185764 A253916

Adjacent sequences: A235009 A235010 A235011 * A235013 A235014 A235015

Keyword

nonn

Author

R. H. Hardin, Jan 02 2014

Status

approved