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 A229440 Number of n X 3 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing. 1
 5, 10, 22, 53, 128, 293, 625, 1244, 2327, 4124, 6976, 11335, 17786, 27071, 40115, 58054, 82265, 114398, 156410, 210601, 279652, 366665, 475205, 609344, 773707, 973520, 1214660, 1503707, 1847998, 2255683, 2735783, 3298250, 3954029, 4715122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA Empirical: a(n) = (1/360)*n^6 + (1/120)*n^5 + (1/36)*n^4 + (5/24)*n^3 - (11/360)*n^2 + (167/60)*n + 2. Conjectures from Colin Barker, Sep 17 2018: (Start) G.f.: x*(5 - 25*x + 57*x^2 - 66*x^3 + 44*x^4 - 15*x^5 + 2*x^6) / (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: ..0..2..2....0..2..2....0..2..2....0..2..2....0..2..2....0..2..2....0..2..2 ..1..0..2....0..2..2....1..0..2....0..2..2....0..2..2....1..0..0....1..0..2 ..1..0..2....1..0..2....1..0..2....1..0..2....0..2..2....1..1..1....1..1..0 ..1..0..2....2..1..0....1..1..0....1..1..0....1..0..2....2..2..2....1..1..0 CROSSREFS Column 3 of A229445. Sequence in context: A087746 A064694 A264147 * A067622 A196240 A341638 Adjacent sequences: A229437 A229438 A229439 * A229441 A229442 A229443 KEYWORD nonn AUTHOR R. H. Hardin, Sep 23 2013 STATUS approved

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Last modified March 31 18:05 EDT 2023. Contains 361672 sequences. (Running on oeis4.)