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A215172 a(0)=1, a(n) = a(n-1)*4^n + 2^n - 1. That is, add n 0's and n 1's to the binary representation of previous term.

%I A215172 #12 Nov 10 2024 13:18:48
%S A215172 1,5,83,5319,1361679,1394359327,5711295803455,93573870443806847,
%T A215172 6132457173405325525247,1607586853265165654490350079,
%U A215172 1685676992249374341322873324438527,7070241751299519797307892876185811552255
%N A215172 a(0)=1, a(n) = a(n-1)*4^n + 2^n - 1. That is, add n 0's and n 1's to the binary representation of previous term.
%C A215172 Binary representations:
%C A215172 a(0) 1
%C A215172 a(1) 101
%C A215172 a(2) 1010011
%C A215172 a(3) 1010011000111
%C A215172 a(4) 101001100011100001111
%C A215172 a(5) 1010011000111000011110000011111
%C A215172 a(6) 1010011000111000011110000011111000000111111
%C A215172 a(7) 101001100011100001111000001111100000011111100000001111111
%C A215172 a(8) 1010011000111000011110000011111000000111111000000011111110000000011111111
%H A215172 Harvey P. Dale, <a href="/A215172/b215172.txt">Table of n, a(n) for n = 0..57</a>
%F A215172 a(0)=1, a(n) = a(n-1)*4^n + 2^n - 1.
%t A215172 nxt[{n_,a_}]:={n+1,FromDigits[Join[IntegerDigits[a],PadRight[{},n,0], PadRight[ {},n,1]]]}; FromDigits[IntegerDigits[#],2]&/@NestList[nxt,{1,1},12][[All,2]] (* _Harvey P. Dale_, Apr 30 2019 *)
%o A215172 (Python)
%o A215172 a = 1
%o A215172 for n in range(1,13):
%o A215172     print(a, end=', ')
%o A215172     a = a*(4**n) + 2**n - 1
%Y A215172 Cf. A076131:  add n 0's and one 1 to the binary representation of previous term.
%K A215172 nonn,base
%O A215172 0,2
%A A215172 _Alex Ratushnyak_, Aug 05 2012