A208101 Triangle read by rows: T(n,0) = 1; for n > 0: T(n,1) = n, for n>1: T(n,n) = T(n-1,n-2); T(n,k) = T(n-2,k-1) + T(n-1,k) for k: 1 < k < n.

1, 1, 1, 1, 2, 1, 1, 3, 2, 2, 1, 4, 3, 5, 2, 1, 5, 4, 9, 5, 5, 1, 6, 5, 14, 9, 14, 5, 1, 7, 6, 20, 14, 28, 14, 14, 1, 8, 7, 27, 20, 48, 28, 42, 14, 1, 9, 8, 35, 27, 75, 48, 90, 42, 42, 1, 10, 9, 44, 35, 110, 75, 165, 90, 132, 42, 1, 11, 10, 54, 44, 154, 110

Offset

0,5

Comments

Another variant of Pascal's triangle, cf. A007318.

Links

Reinhard Zumkeller, Rows n = 0..150 of triangle, flattened

Index entries for triangles and arrays related to Pascal's triangle

Example

The triangle begins:
0:                    1
1:                  1   1
2:                1   2   1
3:              1   3   2   2
4:            1   4   3   5   2
5:          1   5   4   9   5   5
6:        1   6   5  14   9  14   5
7:      1   7   6  20  14  28  14  14
8:    1   8   7  27  20  48  28  42  14
9:  1   9   8  35  27  75  48  90  42  42

Mathematica

T[_, 0] = 1; T[n_, 1] := n; T[n_, n_] := T[n-1, n-2]; T[n_, k_] /; 1<k<n := T[n, k] = T[n-1, k] + T[n-1, k-2]; Table[T[n, k], {n, 0, 11}, {k, 0, n}]  // Flatten (* Jean-François Alcover, Feb 03 2018 *)

Prog

(Haskell)
a208101 n k = a208101_tabl !! n !! k
a208101_row n = a208101_tabl !! n
a208101_tabl =  iterate
   (\row -> zipWith (+) ([0, 1] ++ init row) (row ++ [0])) [1]

Crossrefs

Cf. A208976 (row sums), A101461 (row max), A208983 (central), A208355 (right edge), A074909.

Sequence in context: A338714 A211161 A348687 * A131333 A120643 A242628

Adjacent sequences: A208098 A208099 A208100 * A208102 A208103 A208104

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Mar 04 2012

Status

approved