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A223963 Number of 3 X n 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

%I A223963 #7 Aug 24 2018 17:04:54
%S A223963 64,707,3471,12311,36028,92734,217144,471994,965172,1874532,3482781,
%T A223963 6225291,10754192,18022648,29393806,46779538,72814768,111073890,
%U A223963 166336539,244910775,355022580,507281450,715232788,996008770,1371090364
%N A223963 Number of 3 X n 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
%C A223963 Row 3 of A223961.
%H A223963 R. H. Hardin, <a href="/A223963/b223963.txt">Table of n, a(n) for n = 1..210</a>
%F A223963 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 A223963 Conjectures from _Colin Barker_, Aug 24 2018: (Start)
%F A223963 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 A223963 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 A223963 (End)
%e A223963 Some solutions for n=3:
%e A223963 ..0..0..1....2..2..2....0..0..2....0..0..2....0..2..3....0..1..3....1..2..2
%e A223963 ..1..1..1....1..2..2....0..2..3....1..1..1....0..1..3....1..2..3....0..1..3
%e A223963 ..0..1..3....1..1..3....3..3..3....1..1..2....0..0..2....1..1..3....0..0..2
%Y A223963 Cf. A223961.
%K A223963 nonn
%O A223963 1,1
%A A223963 _R. H. Hardin_, Mar 29 2013