A156747 - OEIS

%I #19 Sep 08 2022 08:45:41

%S 0,0,0,-1,0,2,2,3,2,2,0,-1,2,0,2,-1,0,4,4,7,6,8,6,7,4,4,0,-1,4,2,6,3,

%T 6,2,4,-1,0,6,6,11,10,14,12,15,12,14,10,11,6,6,0,-1,6,4,10,7,12,8,12,

%U 7,10,4,6,-1,0,8,8,15,14,20,18,23,20,24,20,23,18,20,14,15,8,8,0,-1,8,6,14,11

%N a(1) = a(2) = a(3) = 0, then a(n) = abs(a(n-1) + 2*a(n-2) - a(n-3)) - a(n-2) - 1.

%C A jumping flea sequence of order 3 (take a look at the graph and see A104156 for a sequence of order 2).

%C For n>=1, a(n^2 + (3/2)*(1 - (-1)^n)) = -1; for n>=5, a(n^2 - 2 + (1+(-1)^n)/2) = 0; between zeros there are simple patterns.

%H Harvey P. Dale, <a href="/A156747/b156747.txt">Table of n, a(n) for n = 1..1000</a>

%t RecurrenceTable[{a[1]==a[2]==a[3]==0,a[n]==Abs[a[n-1]+2a[n-2]-a[n-3]]-a[n-2]-1},a,{n,90}] (* _Harvey P. Dale_, Aug 19 2019 *)

%o (Magma)

%o a:= func< n | n lt 4 select 0 else Abs(Self(n-1) +2*Self(n-2) -Self(n-3)) -Self(n-2) -1 >;

%o [a(n): n in [1..100]]; // _G. C. Greubel_, Jun 16 2021

%o (Sage)

%o @CachedFunction

%o def a(n): return 0 if (n<4) else abs(a(n-1) +2*a(n-2) -a(n-3)) -a(n-2) -1

%o [a(n) for n in (1..100)] # a=A156747 # _G. C. Greubel_, Jun 16 2021

%Y Cf. A104156, A156748.

%K sign

%O 1,6

%A _Benoit Cloitre_, Feb 14 2009