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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 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

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Last modified November 26 12:09 EST 2022. Contains 358359 sequences. (Running on oeis4.)