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A324665 Starting at n, a(n) is the total number of negative positions visited according to the following rules. On the k-th step (k=1,2,3,...) move a distance of k in the direction of zero. If the number landed on has been landed on before, move a distance of k away from zero instead.

%I A324665 #9 Mar 11 2019 20:43:37
%S A324665 0,0,2,0,17,17,0,939,6,6,0,8,73,73,7,0,48,445544,10,10,57947,0,30,16,
%T A324665 16,782680,11,11,0,184,2650008,232081,232079,232079,232079,12,0,35,
%U A324665 109811,109809,123,17,15,15,577,0,82,62,62,45,45,104,32,16,16,0,281,279
%N A324665 Starting at n, a(n) is the total number of negative positions visited according to the following rules. On the k-th step (k=1,2,3,...) move a distance of k in the direction of zero. If the number landed on has been landed on before, move a distance of k away from zero instead.
%H A324665 David Nacin, <a href="/A324665/a324665.png">A324665(n)/A228474(n)</a>
%e A324665 For n=2, the points visited are 2,1,-1,-4,0.  As exactly two of these are negative, we have a(2)=2.
%o A324665 (Python)
%o A324665 #Sequences A324660-A324692 generated by manipulating this trip function
%o A324665 #spots - positions in order with possible repetition
%o A324665 #flee - positions from which we move away from zero with possible repetition
%o A324665 #stuck - positions from which we move to a spot already visited with possible repetition
%o A324665 def trip(n):
%o A324665     stucklist = list()
%o A324665     spotsvisited = [n]
%o A324665     leavingspots = list()
%o A324665     turn = 0
%o A324665     forbidden = {n}
%o A324665     while n != 0:
%o A324665         turn += 1
%o A324665         sign = n // abs(n)
%o A324665         st = sign * turn
%o A324665         if n - st not in forbidden:
%o A324665             n = n - st
%o A324665         else:
%o A324665             leavingspots.append(n)
%o A324665             if n + st in forbidden:
%o A324665                 stucklist.append(n)
%o A324665             n = n + st
%o A324665         spotsvisited.append(n)
%o A324665         forbidden.add(n)
%o A324665     return {'stuck':stucklist, 'spots':spotsvisited,
%o A324665                 'turns':turn, 'flee':leavingspots}
%o A324665 #Actual sequence
%o A324665 def a(n):
%o A324665     d = trip(n)
%o A324665     return sum(1 for i in d['spots'] if i < 0)
%Y A324665 Cf. A228474, A324660-A324692
%K A324665 nonn
%O A324665 0,3
%A A324665 _David Nacin_, Mar 10 2019