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.

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

R. H. Hardin, Table of n, a(n) for n = 1..112

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

Adjacent sequences: A270603 A270604 A270605 * A270607 A270608 A270609

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 20 2016

Status

approved