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A214906 T(n,k)=Number of nXnXn triangular 0..k arrays with every horizontal row nondecreasing and having the same average value.

%I A214906 #6 Jul 22 2025 23:20:00
%S A214906 2,3,2,4,4,2,5,6,6,2,6,9,14,14,2,7,12,29,50,38,2,8,16,50,182,242,146,
%T A214906 2,9,20,88,458,1802,1682,578,2,10,25,136,1184,7550,29162,13442,2882,2,
%U A214906 11,30,209,2490,31412,210914,657722,134402,14402,2,12,36,302,5213,100350
%N A214906 T(n,k)=Number of nXnXn triangular 0..k arrays with every horizontal row nondecreasing and having the same average value.
%C A214906 Table starts
%C A214906 .2..3...4....5....6.....7......8......9.....10......11......12.......13
%C A214906 .2..4...6....9...12....16.....20.....25.....30......36......42.......49
%C A214906 .2..6..14...29...50....88....136....209....302.....430.....584......793
%C A214906 .2.14..50..182..458..1184...2490...5213...9722...17864...30284....51088
%C A214906 .2.38.242.1802.7550.31412.100350.310079.811472.2065406.4695974.10458806
%H A214906 R. H. Hardin, <a href="/A214906/b214906.txt">Table of n, a(n) for n = 1..1004</a>
%F A214906 Empirical for row n:
%F A214906 n=1: a(k)=2*a(k-1)-a(k-2)
%F A214906 n=2: a(k)=2*a(k-1)-2*a(k-3)+a(k-4)
%F A214906 n=3: a(k)=2*a(k-2)+2*a(k-3)-4*a(k-5)-3*a(k-6)+3*a(k-8)+4*a(k-9)-2*a(k-11)-2*a(k-12)+a(k-14)
%F A214906 n=4: (order 62 symmetric)
%e A214906 Some solutions for n=4 k=4
%e A214906 .....3........2........2........3........2........2........2........2
%e A214906 ....2.4......2.2......1.3......2.4......1.3......2.2......1.3......1.3
%e A214906 ...2.3.4....0.3.3....0.3.3....1.4.4....1.1.4....2.2.2....0.3.3....1.2.3
%e A214906 ..2.3.3.4..1.2.2.3..0.2.3.3..3.3.3.3..0.0.4.4..1.1.2.4..2.2.2.2..0.2.2.4
%Y A214906 Column 2 is A010551(n+1)+2
%Y A214906 Row 2 is A002620(n+2)
%K A214906 nonn,tabl
%O A214906 1,1
%A A214906 _R. H. Hardin_ Jul 29 2012