A208638 Number of 3 X n 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

4, 13, 32, 71, 150, 309, 628, 1267, 2546, 5105, 10224, 20463, 40942, 81901, 163820, 327659, 655338, 1310697, 2621416, 5242855, 10485734, 20971493, 41943012, 83886051, 167772130, 335544289, 671088608, 1342177247, 2684354526, 5368709085

Offset: 1

Author

R. H. Hardin, Feb 29 2012

Keywords

• nonn

Comments

Row 3 of A208637. Possibly row 4 of the convolution array A213568. - Clark Kimberling, Jun 20 2012

From Noah Carey, Aug 31 2021: (Start)

Conjecture: a(n) is equal to half the sum along the edges of (centered, height 2, width n, starting at line n+1) rectangles in Pascal's triangle, as shown here for n=3 (not including the terms inside the rectangles):

1

1 1

1 2 1 a(3) = (4+6+4 + 15+20+15)/2

1 3 3 1

1 4---6---4 1

1 5 | | 5 1

1 6 15--20--15 6 1

1 7 21 35 35 20 7 1 (End)

Examples

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

Links

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

Crossrefs

Cf. A208637.

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).

Conjectures from Colin Barker, Mar 07 2018: (Start)

G.f.: x*(4 - 3*x) / ((1 - x)^2*(1 - 2*x)).

a(n) = 5*2^n - n - 5.

(End)