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A214353 Number of 3 X 3 X 3 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors. 1
26, 169, 660, 1951, 4822, 10507, 20840, 38421, 66802, 110693, 176188, 271011, 404782, 589303, 838864, 1170569, 1604682, 2164993, 2879204, 3779335, 4902150, 6289603, 7989304, 10055005, 12547106, 15533181, 19088524, 23296715, 28250206 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 3 of A214352.

LINKS

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

FORMULA

Empirical: a(n) = (1/36)*n^6 + (7/15)*n^5 + (25/9)*n^4 + (15/2)*n^3 + (331/36)*n^2 + (151/30)*n + 1.

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

G.f.: x*(26 - 13*x + 23*x^2 - 30*x^3 + 20*x^4 - 7*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

EXAMPLE

Some solutions for n=3:

....1......1......2......1......2......1......3......2......3......2......0

...2.0....1.1....2.1....1.1....2.2....1.2....3.1....0.3....0.3....1.3....1.0

..3.2.0..0.3.1..3.1.3..0.3.0..2.2.0..2.1.2..3.1.0..0.3.2..0.1.3..1.2.3..3.1.0

CROSSREFS

Cf. A214352.

Sequence in context: A006354 A249292 A279744 * A283567 A037052 A156339

Adjacent sequences:  A214350 A214351 A214352 * A214354 A214355 A214356

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 13 2012

STATUS

approved

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Last modified June 21 17:44 EDT 2021. Contains 345365 sequences. (Running on oeis4.)