OFFSET
1,2
COMMENTS
Row n consists of 2n-1 positive integers.
EXAMPLE
First seven rows:
1
2 2 2
3 4 7 2 2
4 6 12 8 6 2 2
5 8 17 14 15 6 6 2 2
6 10 22 20 24 16 12 6 6 2 2
7 12 27 26 33 26 25 12 12 6 6 2 2
For n=2, there are 6 triples (x,y,z) having x <= z:
111: |x-y| + |y-z| = 0
112: |x-y| + |y-z| = 1
121: |x-y| + |y-z| = 2
122: |x-y| + |y-z| = 1
212: |x-y| + |y-z| = 2
222: |x-y| + |y-z| = 0
so that row 1 of the array is (2,2,2), representing two 0s, two 1s, and two 2s.
MATHEMATICA
t1[n_] := t1[n] = Tuples[Range[n], 3];
t[n_] := t[n] = Select[t1[n], #[[1]] <= #[[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}];
v = Flatten[u] (* sequence *)
Column[Table[Length[a[n, k]], {n, 1, 15}, {k, 0, 2 n - 2}]] (* array *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Jan 22 2024
STATUS
approved