Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Aug 28 2018 15:02:04
%S 8,36,89,187,373,702,1252,2130,3479,5486,8391,12497,18181,25906,36234,
%T 49840,67527,90242,119093,155367,200549,256342,324688,407790,508135,
%U 628518,772067,942269,1142997,1378538,1653622,1973452,2343735,2770714
%N Number of 3 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.
%C Row 3 of A224158.
%H R. H. Hardin, <a href="/A224159/b224159.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/720)*n^6 + (1/240)*n^5 + (47/144)*n^4 - (3/16)*n^3 + (1111/180)*n^2 - (199/60)*n + 20 for n>2.
%F Conjectures from _Colin Barker_, Aug 28 2018: (Start)
%F G.f.: x*(8 - 20*x + 5*x^2 + 40*x^3 - 47*x^4 - 5*x^5 + 41*x^6 - 27*x^7 + 6*x^8) / (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>9.
%F (End)
%e Some solutions for n=3:
%e ..0..0..1....0..0..1....0..0..0....0..1..0....1..0..0....0..1..1....1..1..0
%e ..1..1..0....1..1..0....0..0..0....1..0..0....0..1..0....1..1..1....1..0..0
%e ..1..1..1....1..1..0....1..0..0....0..1..0....1..0..0....1..1..0....1..1..0
%Y Cf. A224158.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 31 2013