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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
11
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, 2, 9, 20, 88, 458, 1802, 1682, 578, 2, 10, 25, 136, 1184, 7550, 29162, 13442, 2882, 2, 11, 30, 209, 2490, 31412, 210914, 657722, 134402, 14402, 2, 12, 36, 302, 5213, 100350
OFFSET
1,1
COMMENTS
Table starts
.2..3...4....5....6.....7......8......9.....10......11......12.......13
.2..4...6....9...12....16.....20.....25.....30......36......42.......49
.2..6..14...29...50....88....136....209....302.....430.....584......793
.2.14..50..182..458..1184...2490...5213...9722...17864...30284....51088
.2.38.242.1802.7550.31412.100350.310079.811472.2065406.4695974.10458806
LINKS
FORMULA
Empirical for row n:
n=1: a(k)=2*a(k-1)-a(k-2)
n=2: a(k)=2*a(k-1)-2*a(k-3)+a(k-4)
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)
n=4: (order 62 symmetric)
EXAMPLE
Some solutions for n=4 k=4
.....3........2........2........3........2........2........2........2
....2.4......2.2......1.3......2.4......1.3......2.2......1.3......1.3
...2.3.4....0.3.3....0.3.3....1.4.4....1.1.4....2.2.2....0.3.3....1.2.3
..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
CROSSREFS
Column 2 is A010551(n+1)+2
Row 2 is A002620(n+2)
Sequence in context: A105079 A338162 A215182 * A274228 A321476 A214567
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Jul 29 2012
STATUS
approved