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A229424 Number of n X 4 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing. 2
12, 55, 222, 754, 2204, 5700, 13345, 28794, 58053, 110550, 200533, 348855, 585211, 950897, 1502166, 2314261, 3486210, 5146473, 7459536, 10633552, 14929134, 20669410, 28251455, 38159220, 50978083, 67411152, 88297455, 114632157 (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) = (1/8064)*n^8 + (1/288)*n^7 + (103/2880)*n^6 + (17/90)*n^5 + (751/1152)*n^4 + (571/288)*n^3 + (7769/3360)*n^2 + (153/40)*n + 3.

Conjectures from Colin Barker, Sep 15 2018: (Start)

G.f.: x*(12 - 53*x + 159*x^2 - 272*x^3 + 302*x^4 - 222*x^5 + 103*x^6 - 27*x^7 + 3*x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

EXAMPLE

Some solutions for n=4:

..2..2..1..0....1..1..0..0....2..1..0..0....1..1..1..0....1..0..0..0

..2..2..2..1....2..1..0..0....2..2..1..1....2..1..1..0....2..1..0..0

..2..2..2..1....2..1..1..1....2..2..1..1....2..2..1..0....2..1..1..1

..2..2..2..1....2..2..2..2....2..2..2..2....2..2..2..1....2..1..1..1

CROSSREFS

Column 4 of A229428.

Sequence in context: A275249 A143856 A207102 * A009653 A133001 A104188

Adjacent sequences:  A229421 A229422 A229423 * A229425 A229426 A229427

KEYWORD

nonn

AUTHOR

R. H. Hardin, Sep 22 2013

STATUS

approved

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Last modified April 18 22:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)