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

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

Author

R. H. Hardin Jul 29 2012

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..1004

Crossrefs

Column 2 is A010551(n+1)+2

Row 2 is A002620(n+2)

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)