login
A368434
Irregular triangular array T, read by rows: T(n,k) = number of sums |x-y|+|y-z| = k, where x,y,z are in {0,1,...,n}.
14
1, 2, 4, 2, 3, 8, 10, 4, 2, 4, 12, 18, 16, 8, 4, 2, 5, 16, 26, 28, 24, 12, 8, 4, 2, 6, 20, 34, 40, 40, 32, 18, 12, 8, 4, 2, 7, 24, 42, 52, 56, 52, 42, 24, 18, 12, 8, 4, 2, 8, 28, 50, 64, 72, 72, 66, 52, 32, 24, 18, 12, 8, 4, 2, 9, 32, 58, 76, 88, 92, 90, 80
OFFSET
1,2
COMMENTS
Row n consists of 2n-1 positive integers having sum A000575(n) = n^3.
EXAMPLE
First eight rows:
1
2 4 2
3 8 10 4 2
4 12 18 16 8 4 2
5 16 26 28 24 12 8 4 2
6 20 34 40 40 32 18 12 8 4 2
7 24 42 52 56 52 42 24 18 12 8 4 2
8 28 50 64 72 72 66 52 32 24 18 12 8 4 2
MATHEMATICA
t[n_] := t[n] = Tuples[Range[n], 3];
a[n_, k_] := Select[t[n], Abs[#[[1]] - #[[2]]] + Abs[#[[2]] - #[[3]]] == k &];
u = Table[Length[a[n, k]], {n, 1, 15}, {k, 0, 2 n - 2}];
Flatten[u] (* sequence *)
Column[u] (* array *)
CROSSREFS
Cf. A000575, A007590 (limiting reversed row), A368435 (reversed rows), A368435, A368346.
Sequence in context: A141387 A349400 A335678 * A134400 A016095 A298309
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Dec 25 2023
STATUS
approved