OFFSET
1,1
COMMENTS
Row n consists of 2n even positive integers.
EXAMPLE
First six rows:
2 2
4 8 4 2
6 14 14 8 4 2
8 20 24 22 12 8 4 2
10 26 34 36 30 18 12 8 4 2
12 32 44 50 48 40 24 18 12 8 4 2
For n=2, there are 4 triples (x,y,z) having x != y:
121: |x-y| + |y-z| = 2
122: |x-y| + |y-z| = 1
211: |x-y| + |y-z| = 1
212: |x-y| + |y-z| = 2,
so that row 2 of the array is (2,2), representing two 1s and two 2s.
MATHEMATICA
t1[n_] := t1[n] = Tuples[Range[n], 3];
t[n_] := t[n] = Select[t1[n], #[[1]] != #[[2]] &];
a[n_, k_] := Select[t[n], Abs[#[[1]] - #[[2]]] + Abs[#[[2]] - #[[3]]] == k &];
u = Table[Length[a[n, k]], {n, 2, 15}, {k, 1, 2 n - 2}];
v = Flatten[u]; (* sequence *)
Column[Table[Length[a[n, k]], {n, 2, 15}, {k, 1, 2 n - 2}]] (* array *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Dec 31 2023
STATUS
approved