A223719 - OEIS

%I #7 Feb 19 2018 09:27:52

%S 9,81,484,2116,7396,21904,57121,134689,292681,594441,1140624,2085136,

%T 3655744,6180196,10118761,16104169,24990001,37908649,56340036,

%U 82192356,117896164,166513216,231861529,318658201,432681601,580954609,771950656

%N Number of n X 2 0..2 arrays with rows, antidiagonals and columns unimodal.

%C Column 2 of A223725.

%H R. H. Hardin, <a href="/A223719/b223719.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/576)*n^8 + (1/48)*n^7 + (41/288)*n^6 + (13/24)*n^5 + (793/576)*n^4 + (31/16)*n^3 + (119/48)*n^2 + (3/2)*n + 1.

%F Conjectures from _Colin Barker_, Feb 19 2018: (Start)

%F G.f.: x*(9 + 79*x^2 - 80*x^3 + 106*x^4 - 68*x^5 + 31*x^6 - 8*x^7 + 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 ..1..0....2..0....1..2....2..0....1..1....2..0....0..2....2..1....1..1....2..2

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 26 2013