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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

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

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)

EXAMPLE

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

CROSSREFS

Column 3 of A253011.

Sequence in context: A254701 A086577 A193152 * A128961 A218130 A321635

Adjacent sequences:  A253003 A253004 A253005 * A253007 A253008 A253009

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 25 2014

STATUS

approved

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Last modified June 19 07:33 EDT 2019. Contains 324218 sequences. (Running on oeis4.)