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A271035 Number of 3 X 3 X 3 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once. 1
10, 72, 294, 896, 2268, 5040, 10164, 19008, 33462, 56056, 90090, 139776, 210392, 308448, 441864, 620160, 854658, 1158696, 1547854, 2040192, 2656500, 3420560, 4359420, 5503680, 6887790, 8550360, 10534482, 12888064, 15664176, 18921408 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = (1/60)*n^6 + (7/30)*n^5 + (5/4)*n^4 + (19/6)*n^3 + (56/15)*n^2 + (8/5)*n.

Conjectures from Colin Barker, Jan 30 2019: (Start)

G.f.: 2*x*(5 + x) / (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=4:

....1......4......0......3......0......0......0......1......3......1......0

...0.1....2.4....2.4....0.4....2.1....0.0....0.0....0.2....0.3....1.1....2.2

..3.3.3..4.4.4..1.4.4..3.4.4..2.2.2..2.2.1..2.3.0..1.3.4..3.3.3..0.2.2..4.2.2

CROSSREFS

Row 3 of A271034.

Sequence in context: A221548 A037579 A166791 * A108276 A264159 A228316

Adjacent sequences:  A271032 A271033 A271034 * A271036 A271037 A271038

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 29 2016

STATUS

approved

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Last modified May 7 09:12 EDT 2021. Contains 343638 sequences. (Running on oeis4.)