A235013 Number of (n+1) X (4+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).

680, 1112, 1912, 3560, 6856, 13912, 28968, 62600, 138360, 314376, 728008, 1720088, 4123816, 10024648, 24620856, 61022408, 152276808, 382191000, 963411496, 2437205768, 6182237176, 15716144392, 40019084232, 102038360216, 260435212968

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) + a(n-2) - 38*a(n-3) + 33*a(n-4) + 97*a(n-5) - 127*a(n-6) - 88*a(n-7) + 154*a(n-8) + 12*a(n-9) - 48*a(n-10).

Empirical g.f.: 8*x*(85 - 286*x - 541*x^2 + 2341*x^3 + 870*x^4 - 6741*x^5 + 404*x^6 + 7812*x^7 - 1320*x^8 - 2800*x^9) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)*(1 - x - 4*x^2)). - Colin Barker, Oct 17 2018

Example

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

Crossrefs

Column 4 of A235017.

Sequence in context: A257828 A253695 A253702 * A154036 A185765 A206015

Adjacent sequences: A235010 A235011 A235012 * A235014 A235015 A235016

Keyword

nonn

Author

R. H. Hardin, Jan 02 2014

Status

approved