A224410 - OEIS

%I #8 Aug 30 2018 22:40:10

%S 8,36,100,228,465,879,1568,2668,4362,6890,10560,15760,22971,32781,

%T 45900,63176,85612,114384,150860,196620,253477,323499,409032,512724,

%U 637550,786838,964296,1174040,1420623,1709065,2044884,2434128,2883408,3399932

%N Number of 3 X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

%C Row 3 of A224409.

%H R. H. Hardin, <a href="/A224410/b224410.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/720)*n^6 + (1/48)*n^5 + (29/144)*n^4 + (13/16)*n^3 + (2087/360)*n^2 + (7/6)*n.

%F Conjectures from _Colin Barker_, Aug 30 2018: (Start)

%F G.f.: x*(8 - 20*x + 16*x^2 + 4*x^3 - 11*x^4 + 4*x^5) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A224409.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 05 2013