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.

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

Offset: 1

Author

R. H. Hardin, Mar 29 2016

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 3 of A271034.

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)