A253006 Number of n X 3 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 3 and every value increasing by 0 or 1 with every step right, diagonally se or down.
0, 0, 0, 1, 54, 632, 2902, 8416, 18770, 35564, 60398, 94872, 140586, 199140, 272134, 361168, 467842, 593756, 740510, 909704, 1102938, 1321812, 1567926, 1842880, 2148274, 2485708, 2856782, 3263096, 3706250, 4187844, 4709478, 5272752, 5879266
Offset: 1
Keywords
Examples
Some solutions for n=6: ..0..0..0....0..0..0....0..1..2....0..1..2....0..0..1....0..0..0....0..0..1 ..0..0..0....1..1..1....1..1..2....1..1..2....0..1..1....0..0..1....0..0..1 ..0..0..1....1..1..1....1..2..2....1..2..2....1..1..2....1..1..1....0..1..1 ..0..1..1....1..1..1....1..2..2....1..2..2....2..2..2....1..1..2....1..1..2 ..0..1..1....1..2..2....1..2..2....2..2..2....2..2..2....1..2..2....1..1..2 ..1..1..2....1..2..2....1..2..2....2..2..2....2..2..2....2..2..2....1..1..2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Column 3 of A253011.
Formula
Empirical: a(n) = (800/3)*n^3 - 3980*n^2 + (60442/3)*n - 34576 for n>6.
Conjectures from Colin Barker, Dec 08 2018: (Start)
G.f.: x^4*(1 + 50*x + 422*x^2 + 694*x^3 + 385*x^4 + 44*x^5 + 4*x^6) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>10.
(End)