A270850 T(n,k)=Number of nXnXn triangular 0..k arrays with some element plus some adjacent element totalling k+1, k or k-1 exactly once.

0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 24, 30, 0, 0, 0, 66, 270, 252, 0, 0, 0, 120, 1650, 6822, 2298, 0, 0, 0, 198, 7344, 108348, 307494, 28440, 0, 0, 0, 288, 24954, 1144464, 15754872, 27582438, 460494, 0, 0, 0, 402, 68838, 8559378, 469037376, 5805948474, 4875050400

Offset

1,8

Comments

Table starts

.0.0......0..........0.............0................0..................0

.0.0......6.........24............66..............120................198

.0.0.....30........270..........1650.............7344..............24954

.0.0....252.......6822........108348..........1144464............8559378

.0.0...2298.....307494......15754872........469037376.........8746813158

.0.0..28440...27582438....5805948474.....571228600932.....29999932959600

.0.0.460494.4875050400.5281372355106.2104222937252028.358240737864481086

Links

R. H. Hardin, Table of n, a(n) for n = 1..127

Formula

Empirical for row n:

n=1: a(n) = a(n-1)

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
.....3........0........4........3........2........3........0........0
....4.3......0.1......4.4......4.4......4.4......4.4......0.0......1.2
...4.2.4....1.0.1....2.4.3....3.3.3....3.4.4....2.4.4....0.0.0....1.0.0
..3.4.4.3..2.0.1.0..4.2.4.3..2.4.4.3..4.2.4.2..0.4.4.2..2.1.0.2..0.1.1.1

Crossrefs

Sequence in context: A308091 A096527 A028599 * A322379 A225339 A365989

Adjacent sequences: A270847 A270848 A270849 * A270851 A270852 A270853

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 24 2016

Status

approved