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

1,1

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