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 A360595 a(n) is the maximum number of locations 1..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 1..n-1) and a term can be visited up to three times. 5
 0, 3, 1, 2, 2, 12, 1, 2, 2, 4, 2, 10, 15, 1, 2, 2, 4, 2, 10, 20, 1, 2, 2, 4, 2, 10, 13, 8, 2, 10, 2, 15, 7, 15, 25, 17, 53, 1, 2, 2, 4, 2, 10, 65, 1, 2, 2, 4, 2, 10, 13, 8, 2, 10, 2, 15, 7, 15, 72, 1, 2, 2, 4, 2, 10, 24, 18, 52 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS When a location is visited more than once, each such visit counts in a(n). a(0)=0 is no terms before n=0 so an empty path. LINKS Table of n, a(n) for n=1..68. EXAMPLE For n=6, the following is the longest chain of jumps starting from i = n-1 = 5, 1 2 3 4 5 location number i 0, 3, 1, 2, 2 a(i) 1<---- ->2 3<---- ------->2 1<---- ->2 3<---- ------->2 1<---- ->2 3<---- It visited the terms 2,1,2,3 three times in a loop, which gives a total of 12 terms, so a(6)=12. PROG (Python) def A(lastn, times=3, 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+1, a[n]) if mode>0: u, q=0, [] while u

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Last modified May 20 08:05 EDT 2024. Contains 372703 sequences. (Running on oeis4.)