A194123 Triangular array: T(n,k)=|C(n+2,k)-C(n+2,k+2)|, 0<=k<=n.

0, 2, 2, 5, 0, 5, 9, 5, 5, 9, 14, 14, 0, 14, 14, 20, 28, 14, 14, 28, 20, 27, 48, 42, 0, 42, 48, 27, 35, 75, 90, 42, 42, 90, 75, 35, 44, 110, 165, 132, 0, 132, 165, 110, 44, 54, 154, 275, 297, 132, 132, 297, 275, 154, 54, 65, 208, 429, 572, 429, 0, 429, 572, 429, 208, 65

Offset: 0

Author

Clark Kimberling, Aug 16 2011

Keywords

• nonn
• tabl

Examples

			Northwest corner:
0
2...2
5...0...5
9...5...5...9
14..14..0...14..14
20..28..14..14..28..20
		

Crossrefs

Cf. A194124.

Programs

Mathematica

T[n_, k_]:=Abs[Binomial[n+2,k]-Binomial[n+2,k+2]]
Flatten[Table[T[n, k], {n, 0, 10}, {k, 0, n}]]
  (* A194123 as a sequence *)
TableForm[Table[T[n, k], {n, 0, 10}, {k, 0, n}]]
  (* A194123 as an array *)