A214540 T(n,k)=Number of nXnXn triangular 0..k arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and every horizontal row having the same average value.

2, 3, 2, 4, 5, 2, 5, 8, 15, 2, 6, 13, 38, 93, 2, 7, 18, 79, 344, 1007, 2, 8, 25, 152, 1181, 5360, 17213, 2, 9, 32, 263, 3198, 35567, 141470, 461465, 2, 10, 41, 418, 7801, 155102, 2280331, 6042900, 19166997, 2, 11, 50, 643, 16752, 562559, 15986168, 292689331

Offset: 1

Author

R. H. Hardin Jul 20 2012

Keywords

• nonn
• tabl

Comments

Table starts

.2....3....4.....5......6......7.......8.......9.......10.....11...12.13.14

.2....5....8....13.....18.....25......32......41.......50.....61...72.85

.2...15...38....79....152....263.....418.....643......942...1329.1832

.2...93..344..1181...3198...7801...16752...33605....62766.111653

.2.1007.5360.35567.155102.562559.1786114.4984385.12779966

Examples

			Some solutions for n=4 k=4
.....3........2........3........3........1........1........2........2
....2.4......2.2......2.4......3.3......2.0......0.2......2.2......2.2
...2.3.4....2.3.1....2.3.4....3.3.3....2.1.0....0.2.1....3.1.2....3.0.3
..3.2.3.4..1.3.0.4..3.2.4.3..4.3.1.4..2.1.1.0..1.0.2.1..3.1.1.3..3.0.3.2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..85

Crossrefs

Row 2 is A000982(n+1)

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: (symmetric, order 30)