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A201348 Number of n X 3 0..1 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor. 1
2, 8, 18, 47, 118, 273, 585, 1174, 2228, 4030, 6992, 11697, 18950, 29839, 45807, 68736, 101044, 145796, 206830, 288899, 397830, 540701, 726037, 964026, 1266756, 1648474, 2125868, 2718373, 3448502, 4342203, 5429243, 6743620, 8324004, 10214208 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 3 of A201353.

LINKS

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

FORMULA

Empirical: a(n) = (1/5040)*n^7 - (1/720)*n^6 + (37/720)*n^5 - (53/144)*n^4 + (239/90)*n^3 - (2927/360)*n^2 + (1931/140)*n - 4 for n>1.

Conjectures from Colin Barker, May 22 2018: (Start)

G.f.: x*(2 - 8*x + 10*x^2 + 15*x^3 - 62*x^4 + 85*x^5 - 59*x^6 + 20*x^7 - 2*x^8) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>9.

(End)

EXAMPLE

Some solutions for n=10:

..0..0..1....0..0..0....0..0..1....0..0..1....0..0..0....0..0..1....0..0..1

..0..0..1....0..1..1....0..1..1....0..0..1....0..1..1....0..0..1....0..0..1

..0..1..0....1..0..0....0..1..1....0..0..1....0..1..1....0..1..0....0..1..0

..0..1..0....1..0..0....1..1..0....0..0..1....0..1..1....0..1..0....0..1..0

..0..1..1....1..0..0....1..1..0....0..1..0....0..1..1....0..1..1....0..1..1

..0..1..1....1..0..0....1..1..1....0..1..0....0..1..1....1..0..1....0..1..1

..1..0..1....1..0..1....1..1..1....0..1..0....0..1..1....1..0..1....0..1..1

..1..0..1....1..0..1....1..1..1....0..1..1....0..1..1....1..0..1....0..1..1

..1..0..1....1..0..1....1..1..1....1..0..0....1..0..0....1..1..0....1..0..0

..1..1..1....1..1..1....1..1..1....1..1..0....1..0..0....1..1..0....1..0..0

CROSSREFS

Cf. A201353.

Sequence in context: A073307 A064009 A246148 * A102713 A249763 A114723

Adjacent sequences:  A201345 A201346 A201347 * A201349 A201350 A201351

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 30 2011

STATUS

approved

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Last modified October 18 01:04 EDT 2019. Contains 328135 sequences. (Running on oeis4.)