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a(n) = ( (-1)^n * Sum_{k=0..n-2} (-1)^k*10^(2^k) + 10^(2^(n-1)) - ((-1)^n+3)/2 )/9.
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%I #26 May 07 2021 05:09:36

%S 1,12,1121,11112212,1111111122221121,11111111111111112222222211112212,

%T 1111111111111111111111111111111122222222222222221111111122221121

%N a(n) = ( (-1)^n * Sum_{k=0..n-2} (-1)^k*10^(2^k) + 10^(2^(n-1)) - ((-1)^n+3)/2 )/9.

%H Seiichi Manyama, <a href="/A325906/b325906.txt">Table of n, a(n) for n = 1..10</a>

%e n | a(n) | A325910(n)

%e --+------------------+-----------------

%e 1 | 1 | 1

%e 2 | 12 | 10

%e 3 | 1121 | 1101

%e 4 | 11112212 | 11110010

%e 5 | 1111111122221121 | 1111111100001101

%t a[n_] := ((-1)^n * Sum[(-1)^k * 10^(2^k), {k, 0, n - 2}] + 10^(2^(n - 1)) - ((-1)^n + 3)/2)/9; Array[a, 7] (* _Amiram Eldar_, May 07 2021 *)

%o (PARI) {a(n) = ((-1)^n*sum(k=0, n-2, (-1)^k*10^2^k)+10^2^(n-1)-((-1)^n+3)/2)/9}

%Y Cf. A325907, A325910.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Sep 08 2019