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

1,1

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)

Links

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

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)

Example

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

Crossrefs

Cf. A208637.

Sequence in context: A363256 A051912 A060099 * A173277 A036420 A266094

Adjacent sequences: A208635 A208636 A208637 * A208639 A208640 A208641

Keyword

nonn

Author

R. H. Hardin, Feb 29 2012

Status

approved