A325055 a(0) = 0, a(1) = 1; a(2*n) = a(n-1) + a(n), a(2*n+1) = a(n+1) - a(n).

0, 1, 1, 0, 2, -1, 1, 2, 2, -3, 1, 2, 0, 1, 3, 0, 4, -5, -1, 4, -2, 1, 3, -2, 2, 1, 1, 2, 4, -3, 3, 4, 4, -9, -1, 4, -6, 5, 3, -6, 2, 3, -1, 2, 4, -5, 1, 4, 0, -1, 3, 0, 2, 1, 3, 2, 6, -7, 1, 6, 0, 1, 7, 0, 8, -13, -5, 8, -10, 5, 3, -10, -2, 11, -1, -2

Offset

0,5

Links

Table of n, a(n) for n=0..75.

Ilya Gutkovskiy, Scatter plot of a(n) up to n=50000

Formula

a(n) = Sum_{k=1..n} a(2*k-1) = Sum_{k=1..n} (-1)^(n-k) * a(2*k).

a(2^k) = 2^floor(k/2).

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = If[EvenQ[n], a[(n - 2)/2] + a[n/2], a[(n + 1)/2] - a[(n - 1)/2]]; Table[a[n], {n, 0, 75}]

Crossrefs

Cf. A001196 (positions of 0's), A002487, A005590, A075825.

Sequence in context: A050167 A047050 A205028 * A325526 A057820 A054012

Adjacent sequences: A325052 A325053 A325054 * A325056 A325057 A325058

Keyword

sign

Author

Ilya Gutkovskiy, Sep 04 2019

Status

approved