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

1,1

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

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

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

Adjacent sequences: A214903 A214904 A214905 * A214907 A214908 A214909

Keyword

nonn,tabl

Author

R. H. Hardin Jul 29 2012

Status

approved