A201634 Triangle read by rows, n>=0, k>=0, T(n,n) = 2^n, T(n,k) = sum_{j=0..k} T(n-1,j) for k=0..n-1.
1, 1, 2, 1, 3, 4, 1, 4, 8, 8, 1, 5, 13, 21, 16, 1, 6, 19, 40, 56, 32, 1, 7, 26, 66, 122, 154, 64, 1, 8, 34, 100, 222, 376, 440, 128, 1, 9, 43, 143, 365, 741, 1181, 1309, 256, 1, 10, 53, 196, 561, 1302, 2483, 3792, 4048, 512, 1, 11, 64, 260, 821, 2123, 4606
Offset: 0
Examples
[0] [1] [1] [1, 2] [2] [1, 3, 4] [3] [1, 4, 8, 8] [4] [1, 5, 13, 21, 16] [5] [1, 6, 19, 40, 56, 32] [6] [1, 7, 26, 66, 122, 154, 64] [7] [1, 8, 34, 100, 222, 376, 440, 128]
Links
- Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened
Crossrefs
Cf. A247023 (mirrored).
Programs
-
Haskell
a201634 n k = a201634_tabl !! n !! k a201634_row n = a201634_tabl !! n a201634_tabl = iterate (\xs -> scanl1 (+) xs ++ [2 * last xs]) [1] -- Reinhard Zumkeller, Sep 20 2014
-
Sage
@CachedFunction def A201634(n, k): if k==n: return 2^n return add(A201634(n-1, j) for j in (0..k)) for n in (0..7) : print([A201634(n, k) for k in (0..n)])
Comments