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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
12
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Jul 20 2012
STATUS
approved