A225895 - OEIS

%I #8 Sep 05 2018 14:54:12

%S 7,33,145,545,1770,5052,12910,30055,64701,130387,248427,451117,785840,

%T 1320222,2148504,3399307,5244979,7912725,11697733,16978521,24234742,

%U 34067696,47223810,64621359,87380713,116858407,154685343,202809445

%N Number of n X 3 binary arrays whose sum with another n X 3 binary array containing no more than a single 1 has rows and columns in lexicographically nondecreasing order.

%H R. H. Hardin, <a href="/A225895/b225895.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/3360)*n^8 + (3/560)*n^7 + (5/144)*n^6 + (7/120)*n^5 + (761/1440)*n^4 + (81/80)*n^3 + (122/63)*n^2 + (89/210)*n + 3.

%F Conjectures from _Colin Barker_, Sep 05 2018: (Start)

%F G.f.: x*(7 - 30*x + 100*x^2 - 160*x^3 + 195*x^4 - 162*x^5 + 82*x^6 - 23*x^7 + 3*x^8) / (1 - x)^9.

%F 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.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Column 3 of A225900.

%K nonn

%O 1,1

%A _R. H. Hardin_, May 20 2013