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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

%I #4 Mar 18 2016 08:03:08

%S 0,0,3,0,6,15,0,21,144,126,0,36,1137,5406,1149,0,63,4584,132474,

%T 369072,14220,0,90,15843,1522068,34889103,47829828,230247,0,129,40392,

%U 12034134,1489277664,22383193638,12072484260,5038371,0,168,95109,65046258

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

%C Table starts

%C ......0...........0..............0.................0....................0

%C ......3...........6.............21................36...................63

%C .....15.........144...........1137..............4584................15843

%C ....126........5406.........132474...........1522068.............12034134

%C ...1149......369072.......34889103........1489277664..........32485734273

%C ..14220....47829828....22383193638.....4560833505432......332450685760224

%C .230247.12072484260.35714928884139.44967908021958960.13296639688401609639

%H R. H. Hardin, <a href="/A270509/b270509.txt">Table of n, a(n) for n = 1..98</a>

%F Empirical for row n:

%F n=2: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)

%F n=3: [order 10]

%F n=4: [order 18]

%F Empirical quasipolynomials for row n:

%F n=2: polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2

%F n=3: polynomial of degree 5 plus a quasipolynomial of degree 3 with period 2

%F n=4: polynomial of degree 9 plus a quasipolynomial of degree 7 with period 2

%e Some solutions for n=3 k=4

%e ....0......0......2......1......0......0......4......0......1......0......2

%e ...2.3....4.0....0.1....1.0....3.3....3.2....3.0....3.2....0.2....2.4....1.2

%e ..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

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Mar 18 2016

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Last modified July 14 16:15 EDT 2024. Contains 374322 sequences. (Running on oeis4.)