A296413 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.

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

Offset: 1

Author

Altug Alkan, Dec 11 2017

Keywords

• nonn
• fini

Comments

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.

Links

• Altug Alkan, Line graph of A296413

Crossrefs

Cf. A278055, A292351, A296440.

Programs

PARI

my(q=vector(100)); 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

Scheme

;; With memoization-macro definec.
(definec (A296413 n) (cond ((< n 1) (error "Dead!")) ((<= n 3) 1) ((= 4 n) 4) ((= 5 n) 3) (else (+ (A296413 (- n (A296413 (- n 1)))) (A296413 (- n (A296413 (- n 2)))) (A296413 (- n (A296413 (- n 3)))))))) ;; Antti Karttunen, Dec 13 2017