login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Triangle read by rows: T(n, k) = 2^(n + k).
1

%I #15 Dec 09 2023 15:36:11

%S 1,2,4,4,8,16,8,16,32,64,16,32,64,128,256,32,64,128,256,512,1024,64,

%T 128,256,512,1024,2048,4096,128,256,512,1024,2048,4096,8192,16384,256,

%U 512,1024,2048,4096,8192,16384,32768,65536,512,1024,2048,4096,8192,16384,32768,65536,131072,262144

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

%F G.f.: 1/((1 - 2*x)*(1 - 4*x*y)). - _Stefano Spezia_, Dec 09 2023

%e [0] [ 1]

%e [1] [ 2, 4]

%e [2] [ 4, 8, 16]

%e [3] [ 8, 16, 32, 64]

%e [4] [ 16, 32, 64, 128, 256]

%e [5] [ 32, 64, 128, 256, 512, 1024]

%e [6] [ 64, 128, 256, 512, 1024, 2048, 4096]

%e [7] [128, 256, 512, 1024, 2048, 4096, 8192, 16384]

%e [8] [256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536]

%t Array[2^Range[#,2#]&,10,0] (* _Paolo Xausa_, Dec 09 2023 *)

%o (Python)

%o from functools import cache

%o @cache

%o def T_row(n: int) -> list[int]:

%o if n == 0: return [1]

%o row = T_row(n - 1) + [0]

%o for k in range(n): row[k] *= 2

%o row[n] = row[n - 1] * 2

%o return row

%o for n in range(11): print(T_row(n))

%Y 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.

%K nonn,tabl

%O 0,2

%A _Peter Luschny_, Dec 09 2023