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A368435
Irregular triangular array T, read by rows: T(n,k) = number of sums |x-y|+|y-z| = 2n-2-k, where x,y,z are in {0,1,...,n}.
2
1, 2, 4, 2, 2, 4, 10, 8, 3, 2, 4, 8, 16, 18, 12, 4, 2, 4, 8, 12, 24, 28, 26, 16, 5, 2, 4, 8, 12, 18, 32, 40, 40, 34, 20, 6, 2, 4, 8, 12, 18, 24, 42, 52, 56, 52, 42, 24, 7, 2, 4, 8, 12, 18, 24, 32, 52, 66, 72, 72, 64, 50, 28, 8, 2, 4, 8, 12, 18, 24, 32, 40
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
2 4 10 8 3
2 4 8 16 18 12 4
2 4 8 12 24 28 26 16 5
2 4 8 12 18 32 40 40 34 20 6
2 4 8 12 18 24 42 52 56 52 42 24 7
2 4 8 12 18 24 32 52 66 72 72 64 50 28 8
MATHEMATICA
t[n_] := t[n] = Tuples[Range[n], 3];
a[n_, k_] := Select[t[n], Abs[#[[1]] - #[[2]]] + Abs[#[[2]] - #[[3]]] == 2n-2-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 row), A368434, A368437.
Sequence in context: A213433 A294354 A144049 * A058384 A255671 A330590
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Dec 25 2023
STATUS
approved