|
| |
|
|
A202440
|
|
Number of (n+2) X 3 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals.
|
|
1
|
|
|
|
80, 138, 224, 338, 484, 666, 888, 1154, 1468, 1834, 2256, 2738, 3284, 3898, 4584, 5346, 6188, 7114, 8128, 9234, 10436, 11738, 13144, 14658, 16284, 18026, 19888, 21874, 23988, 26234, 28616, 31138, 33804, 36618, 39584, 42706, 45988, 49434, 53048, 56834
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Column 1 of A202447.
|
|
|
LINKS
|
R. H. Hardin, Table of n, a(n) for n = 1..210
|
|
|
FORMULA
|
Empirical: a(n) = (2/3)*n^3 + 8*n^2 + (100/3)*n + 34 for n>1.
Conjectures from Colin Barker, May 28 2018: (Start)
G.f.: 2*x*(40 - 91*x + 76*x^2 - 25*x^3 + 2*x^4) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
(End)
|
|
|
EXAMPLE
|
Some solutions for n=4:
1 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0
0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1
1 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0
0 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0
0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0
|
|
|
CROSSREFS
|
Cf. A202447.
Sequence in context: A224547 A204648 A202447 * A248432 A107931 A234134
Adjacent sequences: A202437 A202438 A202439 * A202441 A202442 A202443
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
R. H. Hardin, Dec 19 2011
|
|
|
STATUS
|
approved
|
| |
|
|
