

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 rightupward antidiagonal neighbors.


2



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
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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
1 464 1
1 5   5 1
1 6 152015 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(n1)  5*a(n2) + 2*a(n3).
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: A037235 A051912 A060099 * A173277 A036420 A266094
Adjacent sequences: A208635 A208636 A208637 * A208639 A208640 A208641


KEYWORD

nonn


AUTHOR

R. H. Hardin, Feb 29 2012


STATUS

approved



