A278347 - OEIS

%I #12 Nov 23 2016 09:36:39

%S 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,

%T 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,

%U -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

%N 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.

%C Not cyclic or periodic.

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

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

%C 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.

%H Tristan Cam and Robert G. Wilson v, <a href="/A278347/b278347.txt">Table of n, a(n) for n = 1..10000</a>

%F 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.

%t 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]

%Y Cf. A277778.

%K easy,sign

%O 1,12

%A _Tristan Cam_ and _Robert G. Wilson v_, Nov 18 2016