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

1,1

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

Links

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

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

Example

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

Crossrefs

Cf. A302680, A180662 (Kn11), A084534.

Sequence in context: A123133 A328367 A338085 * A370297 A339947 A206553

Adjacent sequences: A302673 A302674 A302675 * A302677 A302678 A302679

Keyword

nonn

Author

R. H. Hardin, Apr 11 2018

Status

approved