%I #25 Nov 10 2024 13:05:02

%S 0,1,11,183,5871,375775,48099263,12313411455,6304466665215,

%T 6455773865180671,13221424875890015231,54154956291645502388223,

%U 443637401941159955564326911,7268555193403964711965932118015,238176016577461115681699663643131903

%N a(0) = 0, a(n) = a(n - 1)*2^(n + 1) + 2^n - 1. That is, add one 0 and n 1's to the binary representation of previous term.

%H Harvey P. Dale, <a href="/A215203/b215203.txt">Table of n, a(n) for n = 0..80</a>

%F a(0)=0, a(n) = a(n-1)*2^(n+1) + 2^n - 1.

%F a(n)*2 + A076131(n+1) + 1 = 2^A000217(n+1).

%e Binary representations:

%e a(0): 0;

%e a(1): 1;

%e a(2): 1011;

%e a(3): 10110111;

%e a(4): 1011011101111;

%e a(5): 1011011101111011111;

%e a(6): 10110111011110111110111111;

%e a(7): 1011011101111011111011111101111111;

%e a(8): 1011011101111011111011111101111111011111111, etc.

%t nxt[{n_,a_}]:={n+1,FromDigits[Join[IntegerDigits[a,2],PadRight[{0},n+2,1]],2]}; NestList[nxt,{0,0},15][[All,2]] (* _Harvey P. Dale_, Feb 11 2023 *)

%o (Python)

%o a = 0

%o for n in range(1, 10):

%o print(a, end=', ')

%o a = a*(2**(n+1)) + 2**n - 1

%Y Cf. A076131: add n 0's and one 1 to the binary representation of previous term.

%Y Cf. A215172: add n 0's and n 1's to the binary representation of previous term.

%K nonn,base,easy

%O 0,3

%A _Alex Ratushnyak_, Aug 05 2012