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 A360594 a(n) is the maximum number of locations 0..n-1 which can be visited in a single path starting from i=n-1, where jumps from location i to i +- a(i) are permitted (within 0..n-1) and each location can be visited up to 2 times. 3
 0, 2, 1, 2, 4, 3, 8, 1, 2, 2, 4, 2, 8, 5, 4, 6, 13, 14, 14, 13, 13, 16, 22, 3, 17, 16, 20, 13, 13, 24, 22, 15, 24, 15, 14, 17, 14, 4, 15, 18, 23, 26, 28, 13, 16, 30, 28, 14, 15, 17, 16, 19, 16, 33, 18, 33, 32, 35, 39, 38, 40, 38, 39, 39, 36, 39, 38, 39, 41, 52 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS When a location is visited more than once, each such visit counts in a(n). LINKS Table of n, a(n) for n=0..69. EXAMPLE For n=0 there are no locations 0..n-1, so the sole possible path is empty which is a(0) = 0 locations. For n=1, the sole possible path is location 0 twice, 0 -> 0, which is 2 locations a(1) = 2. For n=12, a path of a(12) = 8 locations visited starting from n-1 = 11 is: 11 -> 9 -> 11 -> 9 -> 7 -> 8 -> 10 -> 6 Locations 11 and 9 are visited twice each and the others once. i = 0 1 2 3 4 5 6 7 8 9 10 11 a(i) = 0, 2, 1, 2, 4, 3, 8, 1, 2, 2, 4, 2 2<----2 ---->2 1<----2<---- ->2---->4 8<---------- PROG (Python) def A(lastn, times=2, mode=0): a, n=[0], 0 while n0: if len(d[-1])>v: v, o=len(d[-1]), d[-1][:] if d[-1][-1]-a[d[-1][-1]]>=0: if d[-1].count(d[-1][-1]-a[d[-1][-1]])0: d.append(d[-1][:]) d[-1].append(d[-1][-1]+a[d[-1][-1]]) r=1 if g>0: if r>0: d[-2].append(d[-2][-1]-a[d[-2][-1]]) else: d[-1].append(d[-1][-1]-a[d[-1][-1]]) r=1 if r==0: d.pop() r, g=0, 0 a.append(v) n+=1 if mode==0: print(n, a[n]) if mode>0: u, q=0, [] while u

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Last modified April 21 17:00 EDT 2024. Contains 371874 sequences. (Running on oeis4.)