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A368043
Triangle read by rows: T(n, k) = 2^(n + k).
1
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
0,2
FORMULA
G.f.: 1/((1 - 2*x)*(1 - 4*x*y)). - Stefano Spezia, Dec 09 2023
EXAMPLE
[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]
MATHEMATICA
Array[2^Range[#, 2#]&, 10, 0] (* Paolo Xausa, Dec 09 2023 *)
PROG
(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))
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.
Sequence in context: A189343 A189779 A262338 * A283691 A283130 A295716
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Dec 09 2023
STATUS
approved