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A270509 T(n,k)=Number of nXnXn triangular 0..k arrays with some element plus some adjacent element totalling k+1 exactly once. 13
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 18 2016
STATUS
approved

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Last modified June 14 12:37 EDT 2024. Contains 373400 sequences. (Running on oeis4.)