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a(n) = partial sums of A324672.
33

%I #5 Mar 11 2019 20:46:56

%S 0,0,1,0,1,0,-1,0,1,0,-1,0,1,0,-1,-2,-1,0,-1,-2,-3,-2,-1,0,-1,-2,-1,

%T -2,-3,-2,-1,0,1,2,3,4,3,4,5,4,3,4,3,2,1,0,1,0,1,2,1,0,1,0,-1,-2,-1,0,

%U 1,2,1,0,-1,-2,-3,-4,-5,-4,-5,-6,-7,-6,-5,-4,-3,-2

%N a(n) = partial sums of A324672.

%H David Nacin, <a href="/A324692/a324692.png">A324692</a>

%o (Python)

%o import functools

%o #Sequences A324660-A324691 generated by manipulating this trip function

%o #spots - positions in order with possible repetition

%o #flee - positions from which we move away from zero with possible repetition

%o #stuck - positions from which we move to a spot already visited with possible repetition

%o def trip(n):

%o stucklist = list()

%o spotsvisited = [n]

%o leavingspots = list()

%o turn = 0

%o forbidden = {n}

%o while n != 0:

%o turn += 1

%o sign = n // abs(n)

%o st = sign * turn

%o if n - st not in forbidden:

%o n = n - st

%o else:

%o leavingspots.append(n)

%o if n + st in forbidden:

%o stucklist.append(n)

%o n = n + st

%o spotsvisited.append(n)

%o forbidden.add(n)

%o return {'stuck':stucklist, 'spots':spotsvisited,

%o 'turns':turn, 'flee':leavingspots}

%o def sgn(x):

%o if x:

%o return x//abs(x)

%o return 0

%o @functools.lru_cache(maxsize=None)

%o def A324672(n):

%o d = trip(n)

%o mx=max([i for i in d['spots']])

%o mn=min([i for i in d['spots']])

%o return sgn(mx+mn)

%o #Actual sequence

%o def a(n):

%o return sum(A324672(i) for i in range(n))

%Y Cf. A228474, A324660-A324692.

%K sign

%O 0,16

%A _David Nacin_, Mar 11 2019