A368043 Triangle read by rows: T(n, k) = 2^(n + k).

1, 2, 4, 4, 8, 16, 8, 16, 32, 64, 16, 32, 64, 128, 256, 32, 64, 128, 256, 512, 1024, 64, 128, 256, 512, 1024, 2048, 4096, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144

Offset: 0

Author

Peter Luschny, Dec 09 2023

Keywords

• nonn
• tabl

Examples

			[0]  [  1]
[1]  [  2,   4]
[2]  [  4,   8,  16]
[3]  [  8,  16,  32,    64]
[4]  [ 16,  32,  64,   128,  256]
[5]  [ 32,  64,  128,  256,  512, 1024]
[6]  [ 64, 128,  256,  512, 1024, 2048,  4096]
[7]  [128, 256,  512, 1024, 2048, 4096,  8192, 16384]
[8]  [256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536]
		

Crossrefs

Cf. A000079 (T(n,0)), A004171 (T(n,n-1)), A000302 (T(n,n)), A171476 (row sums), A003683 (alternating row sums), A134353 (antidiagonal sums), A001018 (T(2n, n)), A094014 (T(n, n/2)), A002697.

Programs

Mathematica

Array[2^Range[#,2#]&,10,0] (* Paolo Xausa, Dec 09 2023 *)

Python

from functools import cache
@cache
def T_row(n: int) -> list[int]:
    if n == 0: return [1]
    row = T_row(n - 1) + [0]
    for k in range(n): row[k] *= 2
    row[n] = row[n - 1] * 2
    return row
for n in range(11): print(T_row(n))

Formula

G.f.: 1/((1 - 2*x)*(1 - 4*x*y)). - Stefano Spezia, Dec 09 2023