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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
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: A143856 A207102 A343539 * A009653 A133001 A340517
KEYWORD
nonn
AUTHOR
R. H. Hardin, Sep 22 2013
STATUS
approved

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)