

A194121


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


2



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
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OFFSET

0,1


LINKS



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}]]
TableForm[Table[T[n, k], {n, 0, 10}, {k, 0, n}]]


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



