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

1,1

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

Links

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

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)

Example

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

Crossrefs

Row 2 is A000982(n+1)

Sequence in context: A027749 A226208 A304743 * A214595 A357255 A136181

Adjacent sequences: A214537 A214538 A214539 * A214541 A214542 A214543

Keyword

nonn,tabl

Author

R. H. Hardin Jul 20 2012

Status

approved