A302676 Number of n X 4 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

5, 5, 12, 20, 33, 64, 121, 231, 440, 838, 1597, 3042, 5796, 11042, 21037, 40079, 76357, 145473, 277150, 528017, 1005960, 1916521, 3651291, 6956316, 13252938, 25249049, 48103634, 91645416, 174599746, 332641529, 633737387, 1207375029, 2300250057, 4382358586

Offset: 1

Author

R. H. Hardin, Apr 11 2018

Keywords

• nonn

Comments

Column 4 of A302680.

Empirical: The antidiagonal sums of A084534 lead to the terms of this sequence for n >= 5. - Johannes W. Meijer, Jun 17 2018

Examples

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

Links

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

Crossrefs

Cf. A302680, A180662 (Kn11), A084534.

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) - a(n-4) for n > 8.

Empirical g.f.: x*(5 - 3*x^2 - 2*x^3 - 6*x^4 - 4*x^5 + 3*x^6 + 2*x^7) / (1 - x - 2*x^2 + x^4). - Colin Barker, Jun 17 2018

The data in the range n = 6..210 is matched by h(n) = hypergeom([-n+1, -(1/2)*n, 1/4-(1/2)*n, -(1/2)*n+1/2, -(1/2)*n+3/4], [-n, -(2/3)*n+1, -(2/3)*n+2/3, -(2/3)*n+1/3], -256/27). - Peter Luschny, Aug 24 2018