A325910 a(n) = ( (-1)^(n-1) * Sum_{k=0..n-1} (-1)^k*10^(2^k) - (1-(-1)^n)/2 )/9.

0, 1, 10, 1101, 11110010, 1111111100001101, 11111111111111110000000011110010, 1111111111111111111111111111111100000000000000001111111100001101

Offset: 0

Author

Seiichi Manyama, Sep 08 2019

Keywords

• nonn

Examples

			               1 =        -0 +                1.
              10 =        -1 +               11.
            1101 =       -10 +             1111.
        11110010 =     -1101 +         11111111.
1111111100001101 = -11110010 + 1111111111111111.
================================================
n |           (a(n))_2           | A325912(n-1)
--+------------------------------+-------------
1 |                 1    =     1 |            2
2 |               (10)_2 =     2 |            2
3 |             (1101)_2 =    13 |           14
4 |         (11110010)_2 =   242 |          242
5 | (1111111100001101)_2 = 65293 |        65294
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10

Crossrefs

Cf. A002275, A007088, A325906, A325912.

Programs

Mathematica

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 *)

PARI

{a(n) = ((-1)^(n-1)*sum(k=0, n-1, (-1)^k*10^2^k)-(1-(-1)^n)/2)/9}

Formula

a(n) = -a(n-1) + (10^(2^(n-1)) - 1)/9.

a(n) = A007088(A325912(n-1) - (n mod 2)) for n > 0.