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A270256
T(n,k)=Number of nXnXn triangular 0..k arrays with some element plus some adjacent element totalling k exactly once.
12
0, 0, 0, 0, 12, 0, 0, 24, 66, 0, 0, 48, 768, 468, 0, 0, 72, 4428, 37848, 3612, 0, 0, 108, 14976, 772056, 3280968, 40020, 0, 0, 144, 42750, 7876728, 308256072, 534438768, 601368, 0, 0, 192, 96768, 51535116, 12712991544, 302595682944, 168922341960
OFFSET
1,5
COMMENTS
Table starts
.0.....0.........0............0..............0................0
.0....12........24...........48.............72..............108
.0....66.......768.........4428..........14976............42750
.0...468.....37848.......772056........7876728.........51535116
.0..3612...3280968....308256072....12712991544.....233617868244
.0.40020.534438768.302595682944.67475902622400.4283012188676772
LINKS
FORMULA
Empirical for row n:
n=2: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)
n=3: [order 10]
n=4: [order 18]
Empirical quasipolynomials for row n:
n=2: polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2
n=3: polynomial of degree 5 plus a quasipolynomial of degree 3 with period 2
n=4: polynomial of degree 9 plus a quasipolynomial of degree 7 with period 2
EXAMPLE
Some solutions for n=3 k=4
....0......2......2......2......4......1......3......2......3......0......3
...1.1....1.3....0.0....4.1....4.3....4.0....3.2....2.1....4.3....4.2....1.0
..0.4.4..1.2.0..2.2.1..3.1.2..3.0.2..2.1.0..4.0.1..1.4.2..3.0.3..3.3.4..1.0.2
CROSSREFS
Sequence in context: A368816 A004012 A360223 * A072837 A023917 A359001
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 14 2016
STATUS
approved