A223982 - OEIS

%I #8 Aug 25 2018 16:15:50

%S 50,684,5029,25410,99634,325120,922768,2346883,5462600,11818092,

%T 24045385,46430852,85704412,152105120,260790200,433664645,701719286,

%U 1107976716,1711156645,2590185158,3849685950,5626605920,8098142520,11491155975

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

%C Column 3 of A223987.

%H R. H. Hardin, <a href="/A223982/b223982.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (353/181440)*n^9 + (5/126)*n^8 + (10571/30240)*n^7 + (251/144)*n^6 + (46793/8640)*n^5 + (1565/144)*n^4 + (159679/11340)*n^3 + (715/63)*n^2 + (6491/1260)*n + 1.

%F Conjectures from _Colin Barker_, Aug 25 2018: (Start)

%F G.f.: x*(50 + 184*x + 439*x^2 - 100*x^3 + 259*x^4 - 210*x^5 + 120*x^6 - 45*x^7 + 10*x^8 - x^9) / (1 - x)^10.

%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.

%F (End)

%e Some solutions for n=3:

%e ..0..2..1....0..3..0....0..1..0....2..2..0....0..1..0....1..2..0....0..0..0

%e ..0..3..1....0..3..1....2..2..0....3..2..0....0..1..2....2..2..1....0..1..0

%e ..0..3..1....0..3..1....2..3..2....3..2..2....2..2..3....2..3..3....0..2..1

%Y Cf. A223987.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 30 2013