A270509 T(n,k)=Number of nXnXn triangular 0..k arrays with some element plus some adjacent element totalling k+1 exactly once.

0, 0, 3, 0, 6, 15, 0, 21, 144, 126, 0, 36, 1137, 5406, 1149, 0, 63, 4584, 132474, 369072, 14220, 0, 90, 15843, 1522068, 34889103, 47829828, 230247, 0, 129, 40392, 12034134, 1489277664, 22383193638, 12072484260, 5038371, 0, 168, 95109, 65046258

Offset

1,3

Comments

Table starts

......0...........0..............0.................0....................0

......3...........6.............21................36...................63

.....15.........144...........1137..............4584................15843

....126........5406.........132474...........1522068.............12034134

...1149......369072.......34889103........1489277664..........32485734273

..14220....47829828....22383193638.....4560833505432......332450685760224

.230247.12072484260.35714928884139.44967908021958960.13296639688401609639

Links

R. H. Hardin, Table of n, a(n) for n = 1..98

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......0......2......1......0......0......4......0......1......0......2
...2.3....4.0....0.1....1.0....3.3....3.2....3.0....3.2....0.2....2.4....1.2
..4.0.1..1.0.1..4.3.4..3.2.4..3.4.1..3.0.0..4.2.1..4.4.2..3.2.4..2.1.3..2.0.3

Crossrefs

Sequence in context: A144091 A019145 A059684 * A083350 A002043 A171002

Adjacent sequences: A270506 A270507 A270508 * A270510 A270511 A270512

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 18 2016

Status

approved