login
A215182
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
12
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, 20, 64, 192, 412, 328, 141, 2, 10, 25, 98, 445, 1558, 3216, 1584, 559, 2, 11, 30, 145, 892, 5096, 18940, 36645, 9026, 2231, 2, 12, 36, 210, 1752, 14826, 102958, 364970, 635051
OFFSET
1,1
COMMENTS
Table starts
.2..3..4...5....6....7.....8.....9....10.....11.....12.....13......14......15
.2..4..6...9...12...16....20....25....30.....36.....42.....49......56......64
.2..5.12..22...38...64....98...145...210....291....394....526.....684.....876
.2..9.26..83..192..445...892..1752..3136...5494...9074..14716...22842...34868
.2.17.80.412.1558.5096.14826.39630.97184.223612.482160.991120.1946560.3679402
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-1)-3*a(k-4)+3*a(k-6)-2*a(k-9)+a(k-10)
n=4: (order 39 symmetric)
EXAMPLE
Some solutions for n=4 k=4
.....3........2........1........3........2........3........3........2
....2.4......1.3......0.2......2.4......1.3......2.4......3.3......2.2
...2.3.4....1.2.3....0.1.2....1.4.4....1.1.4....2.3.4....2.3.4....2.2.2
..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
CROSSREFS
Row 2 is A002620(n+2)
Sequence in context: A145178 A105079 A338162 * A214906 A274228 A321476
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Aug 05 2012
STATUS
approved