A271036 Number of 4 X 4 X 4 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.

34, 450, 3114, 15116, 58036, 188034, 535106, 1373944, 3244098, 7143708, 14829100, 29262168, 55258840, 100405196, 176323116, 300384832, 497995586, 805585902, 1274479910, 1975833860, 3006869580, 4498661310, 6625771230, 9618069240

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..96

Formula

Empirical: a(n) = (73/1814400)*n^10 + (169/120960)*n^9 + (1277/60480)*n^8 + (3667/20160)*n^7 + (84829/86400)*n^6 + (3953/1152)*n^5 + (87629/11340)*n^4 + (324707/30240)*n^3 + (104197/12600)*n^2 + (278/105)*n.

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

G.f.: 2*x*(17 + 38*x + 17*x^2 + x^3) / (1 - x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.

(End)

Example

Some solutions for n=4:
.....0........2........2........0........0........0........1........1
....0.1......2.3......2.3......0.0......1.0......0.0......1.1......1.1
...1.2.1....1.3.3....2.3.3....0.2.1....2.3.4....0.0.1....1.1.1....0.1.2
..1.3.3.4..4.4.4.4..4.4.4.3..3.3.3.4..4.4.4.4..3.4.3.4..0.3.3.4..2.2.3.4

Crossrefs

Row 4 of A271034.

Sequence in context: A033914 A189452 A159655 * A244495 A107917 A277226

Adjacent sequences: A271033 A271034 A271035 * A271037 A271038 A271039

Keyword

nonn

Author

R. H. Hardin, Mar 29 2016

Status

approved