|
%I #4 Aug 05 2012 06:14:44
%S 2,3,2,4,4,2,5,6,5,2,6,9,12,9,2,7,12,22,26,17,2,8,16,38,83,80,48,2,9,
%T 20,64,192,412,328,141,2,10,25,98,445,1558,3216,1584,559,2,11,30,145,
%U 892,5096,18940,36645,9026,2231,2,12,36,210,1752,14826,102958,364970,635051
%N T(n,k)=Number of nXnXn triangular 0..k arrays with every horizontal row nondecreasing, first elements of rows nonincreasing, last elements of rows nondecreasing, and every row having the same average value
%C Table starts
%C .2..3..4...5....6....7.....8.....9....10.....11.....12.....13......14......15
%C .2..4..6...9...12...16....20....25....30.....36.....42.....49......56......64
%C .2..5.12..22...38...64....98...145...210....291....394....526.....684.....876
%C .2..9.26..83..192..445...892..1752..3136...5494...9074..14716...22842...34868
%C .2.17.80.412.1558.5096.14826.39630.97184.223612.482160.991120.1946560.3679402
%H R. H. Hardin, <a href="/A215182/b215182.txt">Table of n, a(n) for n = 1..607</a>
%F Empirical for row n:
%F n=1: a(k)=2*a(k-1)-a(k-2)
%F n=2: a(k)=2*a(k-1)-2*a(k-3)+a(k-4)
%F n=3: a(k)=2*a(k-1)-3*a(k-4)+3*a(k-6)-2*a(k-9)+a(k-10)
%F n=4: (order 39 symmetric)
%e Some solutions for n=4 k=4
%e .....3........2........1........3........2........3........3........2
%e ....2.4......1.3......0.2......2.4......1.3......2.4......3.3......2.2
%e ...2.3.4....1.2.3....0.1.2....1.4.4....1.1.4....2.3.4....2.3.4....2.2.2
%e ..1.3.4.4..0.2.2.4..0.0.1.3..1.3.4.4..0.2.2.4..2.2.4.4..2.2.4.4..0.2.2.4
%Y Row 2 is A002620(n+2)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Aug 05 2012
|
