A145865 a(0) = 0, a(1) = 1, a(2n) = a(n), a(2n+1) = a(n) - a(n+1).

0, 1, 1, 0, 1, 1, 0, -1, 1, 0, 1, 1, 0, 1, -1, -2, 1, 1, 0, -1, 1, 0, 1, 1, 0, -1, 1, 2, -1, 1, -2, -3, 1, 0, 1, 1, 0, 1, -1, -2, 1, 1, 0, -1, 1, 0, 1, 1, 0, 1, -1, -2, 1, -1, 2, 3, -1, -2, 1, 3, -2, 1, -3, -4, 1, 1, 0, -1, 1, 0, 1, 1, 0, -1, 1, 2, -1, 1, -2, -3, 1, 0, 1, 1, 0, 1, -1, -2, 1, 1, 0

Offset

0,16

Comments

Variation on Stern's Diatomic Series

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Formula

From Chai Wah Wu, Dec 20 2016: (Start)

a(2^k*n+1) = a(n+1) if k is even

a(2^k*n+1) = a(n)-a(n+1) = a(2n+1) if k is odd

a(2^k*n+2^k-1) = a(n) - k*a(n+1)

a(2^k*n+2^k-3) = a(n+1) for k >= 2

a(2^k*n+2^k-5) = (k-1)*a(n+1)-a(n) for k >= 3

a(2^k*n+2^k-7) = a(n) - (k-2)*a(n+1) for k >= 3

This implies that

a(2^k+1) = 1 if k is even

a(2^k+1) = 0 if k is odd

a(2^k-1) = 2 - k for k >= 1

a(2^k-3) = 1 for k >= 2

a(2^k-5) = k - 3 for k >= 3

a(2^k-7) = 4 - k for k >= 3

(End)

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = If[EvenQ@ n, a[n/2], a[#] - a[# + 1] &[(n - 1)/2]]; Table[a@ n, {n, 0, 85}] (* Michael De Vlieger, Dec 21 2016 *)

Crossrefs

Cf. A002487, A005590.

Sequence in context: A369454 A224444 A101808 * A341281 A076452 A076453

Adjacent sequences: A145862 A145863 A145864 * A145866 A145867 A145868

Keyword

easy,sign

Author

Paolo P. Lava and Giorgio Balzarotti, Oct 22 2008

Status

approved