A245235 Repeat 2^(n*(n+1)/2) n+1 times.

1, 2, 2, 8, 8, 8, 64, 64, 64, 64, 1024, 1024, 1024, 1024, 1024, 32768, 32768, 32768, 32768, 32768, 32768, 2097152, 2097152, 2097152, 2097152, 2097152, 2097152, 2097152, 268435456, 268435456, 268435456, 268435456, 268435456, 268435456, 268435456, 268435456

Offset: 0

Author

Paul Curtz, Jul 14 2014

Keywords

• nonn
• tabl

Comments

For a(n), the successive exponents of 2 are 0, 1, 1, 3, 3, 3,... = A057944(n).

Examples

			n+1 times repeated 2^(n*(n+1)/2)= 1, 2, 8, 64, 1024,... = A139685(n).
By the formula: a(0)=1/1=1, a(1)=2/1=2, a(2)=4/2=2, a(3)=8/1=8, a(4)=16/2=8,...
As triangle:
   1,
   2,    2,
   8,    8,    8,
  64,   64,   64,   64,
1024, 1024, 1024, 1024, 1024,
etc.
Row sums: 1, 4, 24, 256,... = A095340.
		

Crossrefs

Cf. A000079, A006125, A057944, A059268, A095340, A123903, A139685.

Programs

Mathematica

Table[2^(n*(n+1)/2), {n, 0, 7}, {n+1}] // Flatten (* Jean-François Alcover, Jul 15 2014 *)

Python

from math import isqrt
def A245235(n): return 1<<((m:=isqrt(n+1<<3)-1>>1)*(m+1)>>1) # Chai Wah Wu, Dec 17 2024

Formula

a(n) = 2^n/A059268(n).

T(n, k) = 2^(n*(n+1)/2), 0 <= k <= n. - Michel Marcus, Jul 17 2014