A229448 - OEIS

%I #12 Jun 05 2022 12:13:26

%S 17,47,128,324,753,1609,3184,5890,10281,17075,27176,41696,61977,89613,

%T 126472,174718,236833,315639,414320,536444,685985,867345,1085376,

%U 1345402,1653241,2015227,2438232,2929688,3497609,4150613,4897944,5749494,6715825

%N Number of 5 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

%H R. H. Hardin, <a href="/A229448/b229448.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (11/60)*n^5 - (1/2)*n^4 + (15/4)*n^3 - 1*n^2 + (257/30)*n + 6.

%F Conjectures from _Colin Barker_, Sep 17 2018: (Start)

%F G.f.: x*(17 - 55*x + 101*x^2 - 79*x^3 + 44*x^4 - 6*x^5) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Row 5 of A229445.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 23 2013