A325906 -id:A325906 - cp's OEIS frontend

A325907 a(n) = ( (-1)^n * Sum_{k=0..n-2} (-1)^k*10^(2^k) + 10^(2^(n-1)) - ((-1)^n+3)/2 )/3.

3, 36, 3363, 33336636, 3333333366663363, 33333333333333336666666633336636, 3333333333333333333333333333333366666666666666663333333366663363

Offset: 1

Seiichi Manyama, Sep 08 2019

nonn

All terms are elements of A213517.

			              36 =        -3 - 1 +        4 * 10^1.
            3363 =       -36 - 1 +       34 * 10^2.
        33336636 =     -3363 - 1 +     3334 * 10^4.
3333333366663363 = -33336636 - 1 + 33333334 * 10^8.
------------------------------------------------------
T(n) = n*(n+1)/2.
               T(3) =                               6.
              T(36) =                             666.
            T(3363) =                         5656566.
        T(33336636) =                 555665666566566.
T(3333333366663363) = 5555555666655656666556566566566.

Seiichi Manyama, Table of n, a(n) for n = 1..10

Cf. A000217, A062691, A093137, A119219, A213517, A309597, A325906.

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

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

a(n) = 3 * A325906(n).

a(n) = -a(n-1) - 1 + A093137(2^(n-2)) * 10^(2^(n-2)).

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

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Sep 08 2019

nonn

			               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

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

Cf. A002275, A007088, A325906, A325912.

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 *)

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

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

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

cp's OEIS Frontend

A325907 a(n) = ( (-1)^n * Sum_{k=0..n-2} (-1)^k*10^(2^k) + 10^(2^(n-1)) - ((-1)^n+3)/2 )/3.

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