A229422 - OEIS

%I #8 Sep 15 2018 08:45:07

%S 5,12,27,55,102,175,282,432,635,902,1245,1677,2212,2865,3652,4590,

%T 5697,6992,8495,10227,12210,14467,17022,19900,23127,26730,30737,35177,

%U 40080,45477,51400,57882,64957,72660,81027,90095,99902,110487,121890,134152

%N Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.

%H R. H. Hardin, <a href="/A229422/b229422.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (25/12)*n + 2.

%F Conjectures from _Colin Barker_, Sep 15 2018: (Start)

%F G.f.: x*(5 - 13*x + 17*x^2 - 10*x^3 + 2*x^4) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=4:

%e ..0..0....0..0....1..0....0..0....1..1....1..0....0..0....0..0....2..2....0..0

%e ..0..0....1..0....1..0....0..0....2..1....2..1....0..0....1..1....2..2....1..1

%e ..1..1....1..1....1..1....0..0....2..1....2..1....1..0....1..1....2..2....2..2

%e ..2..2....2..1....2..1....1..1....2..2....2..1....1..0....2..1....2..2....2..2

%Y Column 2 of A229428.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 22 2013