A278347 If n is even, a(n) = a(n/2 -1) - a(n/2 +1), and if n is odd, a(n) = a((n-1)/2) - a((n+1)/2), with a(1) = a(2) = 1.

1, 1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 2, 1, 1, 0, -1, -1, -2, -1, -1, 0, -1, -1, 0, 1, 1, 0, 1, 1, 2, 1, 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, 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, 0, 1, 1, 2, 1, 1, 0, 1, 1, 0, -1, -1, 0, -1, -1, -2, -1, -1, 0

Offset

1,12

Comments

Not cyclic or periodic.

-3 < a(n) < 3, for all n < 10^8.

First occurrence of k beginning at -2: 18, 7, 3, 1, 12.

The distribution of a(n) in the first 10^8 terms: -2, 4166621; -1, 33333332; 0, 25000091; 1, 33333335 and 2, 4166621 or -2 1/24, -1 1/3, 0 1/4, 1 1/3 and 2 1/24.

Links

Tristan Cam and Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Formula

a(1) = 1 and a(2) = 1. a(n) = a(n/2 -1) - a(n/2 +1) if n is even and a(n) = a((n-1)/2) - a((n+1)/2) if n is odd.

Mathematica

a[n_] := a[n] = If[ OddQ[n], a[(n - 1)/2] - a[(n + 1)/2], a[n/2 - 1] - a[n/2 + 1]]; a[1] = a[2] = 1; Array[a, 105]

Crossrefs

Cf. A277778.

Sequence in context: A075685 A037906 A319394 * A120936 A335294 A214438

Adjacent sequences: A278344 A278345 A278346 * A278348 A278349 A278350

Keyword

easy,sign

Author

Tristan Cam and Robert G. Wilson v, Nov 18 2016

Status

approved