A223963 - OEIS

%I #7 Aug 24 2018 17:04:54

%S 64,707,3471,12311,36028,92734,217144,471994,965172,1874532,3482781,

%T 6225291,10754192,18022648,29393806,46779538,72814768,111073890,

%U 166336539,244910775,355022580,507281450,715232788,996008770,1371090364

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

%C Row 3 of A223961.

%H R. H. Hardin, <a href="/A223963/b223963.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/8640)*n^9 + (1/320)*n^8 + (503/10080)*n^7 + (659/1440)*n^6 + (3013/960)*n^5 + (37141/2880)*n^4 + (106019/2160)*n^3 - (18977/720)*n^2 + (2711/70)*n - 6 for n>2.

%F Conjectures from _Colin Barker_, Aug 24 2018: (Start)

%F G.f.: x*(64 + 67*x - 719*x^2 + 1736*x^3 - 2287*x^4 + 2271*x^5 - 2070*x^6 + 1632*x^7 - 910*x^8 + 311*x^9 - 58*x^10 + 5*x^11) / (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>12.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A223961.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 29 2013