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%I #36 May 07 2021 05:09:20
%S 0,1,10,1101,11110010,1111111100001101,
%T 11111111111111110000000011110010,
%U 1111111111111111111111111111111100000000000000001111111100001101
%N a(n) = ( (-1)^(n-1) * Sum_{k=0..n-1} (-1)^k*10^(2^k) - (1-(-1)^n)/2 )/9.
%H Seiichi Manyama, <a href="/A325910/b325910.txt">Table of n, a(n) for n = 0..10</a>
%F a(n) = -a(n-1) + (10^(2^(n-1)) - 1)/9.
%F a(n) = A007088(A325912(n-1) - (n mod 2)) for n > 0.
%e 1 = -0 + 1.
%e 10 = -1 + 11.
%e 1101 = -10 + 1111.
%e 11110010 = -1101 + 11111111.
%e 1111111100001101 = -11110010 + 1111111111111111.
%e ================================================
%e n | (a(n))_2 | A325912(n-1)
%e --+------------------------------+-------------
%e 1 | 1 = 1 | 2
%e 2 | (10)_2 = 2 | 2
%e 3 | (1101)_2 = 13 | 14
%e 4 | (11110010)_2 = 242 | 242
%e 5 | (1111111100001101)_2 = 65293 | 65294
%t a[n_] := ((-1)^(n - 1) * Sum[(-1)^k * 10^(2^k), {k, 0, n - 1} ] - (1 - (-1)^n)/2)/9; Array[a, 8, 0] (* _Amiram Eldar_, May 07 2021 *)
%o (PARI) {a(n) = ((-1)^(n-1)*sum(k=0, n-1, (-1)^k*10^2^k)-(1-(-1)^n)/2)/9}
%Y Cf. A002275, A007088, A325906, A325912.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 08 2019