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A296413
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a(1) = a(2) = a(3) = 1, a(4) = 4, a(5) = 3; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 5.
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5
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1, 1, 1, 4, 3, 5, 6, 5, 9, 8, 7, 8, 11, 12, 11, 10, 14, 15, 16, 12, 17, 16, 18, 16, 24, 14, 19, 25, 23, 16, 21, 26, 28, 21, 27, 25, 26, 26, 34, 29, 25, 30, 38, 33, 25, 33, 40, 34, 30, 30, 48, 36, 35, 36, 44, 37, 40, 44, 43, 36, 53, 39, 43, 48, 44, 49, 49, 48, 41, 56, 45, 50, 57, 53, 55, 51, 46, 63, 63, 49, 56, 58, 64, 51
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OFFSET
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1,4
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COMMENTS
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For this recurrence (a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) with five initial conditions, only three options such that 1 <= a(i) <= 5 with 1 <= i <= 5 result in a sequence that does not quickly terminate, of which A278055 is the only well-behaved sequence. The other two sets of initial conditions are (1,1,1,4,3) (which yields this sequence) and (1,1,3,4,4), which yields A292351. This sequence is finite but has a relatively long life: a(509871) = 519293 is its final term since a(509872) refers to a nonpositive index and thus fails to exist; see graph in Links section.
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LINKS
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PROG
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(PARI) q=vector(10^5); q[1]=1; q[2]=1; q[3]=1; q[4]=4; q[5]=3; for(n=6, #q, q[n] = q[n-q[n-1]]+q[n-q[n-2]]+q[n-q[n-3]]); q
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CROSSREFS
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KEYWORD
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nonn,fini
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AUTHOR
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STATUS
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approved
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