A223919 - OEIS

%I #7 Feb 23 2018 11:41:12

%S 6,36,158,548,1600,4102,9503,20299,40570,76704,138348,239630,400700,

%T 649642,1024813,1577669,2376142,3508636,5088714,7260552,10205240,

%U 14148014,19366507,26200111,35060546,46443736,60943096,79264338

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

%C Row 2 of A223918.

%H R. H. Hardin, <a href="/A223919/b223919.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/10080)*n^8 + (1/504)*n^7 + (1/40)*n^6 + (109/720)*n^5 + (259/480)*n^4 + (173/144)*n^3 + (4877/2520)*n^2 + (481/420)*n + 1.

%F Conjectures from _Colin Barker_, Feb 23 2018: (Start)

%F G.f.: x*(6 - 18*x + 50*x^2 - 82*x^3 + 88*x^4 - 62*x^5 + 29*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..2..0....0..0..2....1..0..0....0..0..0....0..1..1....1..2..0....0..1..0

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

%Y Cf. A223918.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 29 2013