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A215203 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.

%I A215203 #25 Nov 10 2024 13:05:02
%S A215203 0,1,11,183,5871,375775,48099263,12313411455,6304466665215,
%T A215203 6455773865180671,13221424875890015231,54154956291645502388223,
%U A215203 443637401941159955564326911,7268555193403964711965932118015,238176016577461115681699663643131903
%N A215203 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 A215203 Harvey P. Dale, <a href="/A215203/b215203.txt">Table of n, a(n) for n = 0..80</a>
%F A215203 a(0)=0, a(n) = a(n-1)*2^(n+1) + 2^n - 1.
%F A215203 a(n)*2 + A076131(n+1) + 1 = 2^A000217(n+1).
%e A215203 Binary representations:
%e A215203 a(0): 0;
%e A215203 a(1): 1;
%e A215203 a(2): 1011;
%e A215203 a(3): 10110111;
%e A215203 a(4): 1011011101111;
%e A215203 a(5): 1011011101111011111;
%e A215203 a(6): 10110111011110111110111111;
%e A215203 a(7): 1011011101111011111011111101111111;
%e A215203 a(8): 1011011101111011111011111101111111011111111, etc.
%t A215203 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 A215203 (Python)
%o A215203 a = 0
%o A215203 for n in range(1, 10):
%o A215203     print(a, end=', ')
%o A215203     a = a*(2**(n+1)) + 2**n - 1
%Y A215203 Cf. A076131:  add n 0's and one 1 to the binary representation of previous term.
%Y A215203 Cf. A215172:  add n 0's and n 1's to the binary representation of previous term.
%K A215203 nonn,base,easy
%O A215203 0,3
%A A215203 _Alex Ratushnyak_, Aug 05 2012