A235293 Number of (n+1) X (3+1) 0..3 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3 (constant-stress 1 X 1 tilings).

272, 476, 832, 1736, 3536, 8336, 18832, 48128, 115952, 312416, 782032, 2180576, 5582576, 15917216, 41303632, 119516768, 312747632, 914077856, 2405006032, 7078411616, 18692677616, 55290785696, 146389598032, 434571648608

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 17*a(n-2) - 57*a(n-3) - 86*a(n-4) + 372*a(n-5) + 76*a(n-6) - 972*a(n-7) + 360*a(n-8) + 864*a(n-9) - 576*a(n-10).

Empirical g.f.: 4*x*(68 - 85*x - 1305*x^2 + 1663*x^3 + 8677*x^4 - 11152*x^5 - 23382*x^6 + 29868*x^7 + 21600*x^8 - 27072*x^9) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)*(1 - 3*x^2)*(1 - 6*x^2)*(1 - 8*x^2)). - Colin Barker, Oct 18 2018

Example

Some solutions for n=5:
  0 0 0 3     2 2 2 1     0 3 0 0     1 2 1 3     3 3 3 3
  3 0 3 3     0 3 0 2     0 0 0 3     3 1 3 2     3 0 3 0
  3 3 3 0     3 3 3 2     0 3 0 0     1 2 1 3     1 1 1 1
  0 3 0 0     0 3 0 2     3 3 3 0     3 1 3 2     0 3 0 3
  0 0 0 3     1 1 1 0     0 3 0 0     1 2 1 3     0 0 0 0
  0 3 0 0     0 3 0 2     3 3 3 0     2 0 2 1     3 0 3 0

Crossrefs

Column 3 of A235301.

Sequence in context: A062906 A253361 A133514 * A270302 A304549 A316374

Adjacent sequences: A235290 A235291 A235292 * A235294 A235295 A235296

Keyword

nonn

Author

R. H. Hardin, Jan 05 2014

Status

approved