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A270606
T(n,k)=Number of nXnXn triangular 0..k arrays with some element plus some adjacent element totalling k+1 or k-1 exactly once.
12
0, 0, 6, 0, 0, 0, 0, 36, 0, 0, 0, 36, 312, 0, 0, 0, 96, 1716, 8808, 0, 0, 0, 120, 8148, 171576, 443088, 0, 0, 0, 204, 23448, 1728288, 46957788, 44168712, 0, 0, 0, 252, 67788, 13177740, 1008327378, 38923001616, 8708857332, 0, 0, 0, 360, 144252, 70129212
OFFSET
1,3
COMMENTS
Table starts
.0.0........0...........0.............0...............0................0
.6.0.......36..........36............96.............120..............204
.0.0......312........1716..........8148...........23448............67788
.0.0.....8808......171576.......1728288........13177740.........70129212
.0.0...443088....46957788....1008327378.....25162747992.....271906503420
.0.0.44168712.38923001616.1749723617976.176610474548304.4288332432901128
LINKS
FORMULA
Empirical for row n:
n=2: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4) for n>5
n=3: [order 10] for n>17
n=4: [order 18] for n>33
Empirical quasipolynomials for row n:
n=2: polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2 for n>1
n=3: polynomial of degree 5 plus a quasipolynomial of degree 3 with period 2 for n>7
n=4: polynomial of degree 9 plus a quasipolynomial of degree 7 with period 2 for n>15
EXAMPLE
Some solutions for n=4 k=4
.....0........0........4........0........0........0........2........3
....0.4......0.1......0.4......0.0......0.0......0.1......0.1......1.1
...0.4.4....3.1.3....1.3.3....4.4.2....0.0.0....0.0.3....0.0.0....1.3.1
..0.0.0.3..1.3.3.4..3.1.1.3..2.0.4.3..0.1.4.2..4.0.1.3..0.4.4.0..0.0.1.3
CROSSREFS
Sequence in context: A339861 A087936 A089804 * A087255 A097606 A201995
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 20 2016
STATUS
approved