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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.)