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

0,3

Comments

Row sums are A014318.

Links

Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

Example

[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]

Prog

(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)])
(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

Crossrefs

Cf. A247023 (mirrored).

Sequence in context: A210231 A180378 A208341 * A210211 A283054 A247358

Adjacent sequences: A201631 A201632 A201633 * A201635 A201636 A201637

Keyword

nonn,tabl

Author

Peter Luschny, Nov 14 2012

Status

approved