A194121 Triangular array: T(n,k)=C(n+2,k)+C(n+2,k+1)+C(n+2,k+2), 0<=k<=n.

4, 7, 7, 11, 14, 11, 16, 25, 25, 16, 22, 41, 50, 41, 22, 29, 63, 91, 91, 63, 29, 37, 92, 154, 182, 154, 92, 37, 46, 129, 246, 336, 336, 246, 129, 46, 56, 175, 375, 582, 672, 582, 375, 175, 56, 67, 231, 550, 957, 1254, 1254, 957, 550, 231, 67, 79, 298, 781

Offset

0,1

Links

Table of n, a(n) for n=0..57.

Formula

T(n,k)=C(n+2,k)+C(n+2,k+1)+C(n+2,k+2), 0<=k<=n.

Example

Northwest corner:
4
7....7
11...14...11
16...25...25...16
22...41...50...41...22
29...63...91...91...63..29

Mathematica

T[n_, k_] := Binomial[n + 2, k] + Binomial[n + 2, k + 1] + Binomial[n + 2, k + 2]
Flatten[Table[T[n, k], {n, 0, 10}, {k, 0, n}]]
  (* A194121 as a sequence *)
TableForm[Table[T[n, k], {n, 0, 10}, {k, 0, n}]]
 (* A194121 as an array *)

Crossrefs

Cf. A194119, A194121.

Sequence in context: A061891 A310931 A310932 * A063194 A071529 A349537

Adjacent sequences: A194118 A194119 A194120 * A194122 A194123 A194124

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 16 2011

Status

approved