A296440 a(1) = 2, a(2) = a(3) = 3, a(4) = 4, a(5) = a(6) = 6; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 6.

2, 3, 3, 4, 6, 6, 7, 8, 8, 9, 9, 10, 11, 13, 13, 12, 14, 16, 16, 14, 19, 17, 18, 19, 21, 21, 20, 22, 23, 24, 23, 24, 25, 26, 26, 27, 27, 28, 29, 30, 30, 31, 32, 34, 33, 34, 35, 37, 36, 37, 39, 36, 39, 42, 39, 41, 41, 44, 45, 41, 40, 50, 46, 48, 43, 48, 51, 49, 49, 54, 48, 53, 51, 58, 50, 58, 52, 57, 56, 59, 57, 60, 58

Offset: 1

Author

Altug Alkan, Dec 12 2017

Keywords

• nonn
• look

Comments

Conjecture: Sequence is infinite.

Links

• Altug Alkan, Table of n, a(n) for n = 1..10000
• Altug Alkan, Scatterplot of a(n)-2*n/3
• Hans Havermann, Scatterplot of a(n) for n <= 10^7

Crossrefs

Cf. A005185, A278055, A284644, A292351.

Programs

Maple

a:= proc(n) option remember; procname(n-procname(n-1))+procname(n-procname(n-2))+procname(n-procname(n-3)) end proc:
a(1):= 2: a(2):= 3: a(3):= 3: a(4):= 4: a(5):= 6: a(6):= 6:
map(a, [$1..100]); # Robert Israel, Dec 12 2017

Mathematica

a[n_] := a[n] = If[n<7, {2, 3, 3, 4, 6, 6}[[n]], a[n - a[n-1]] + a[n - a[n-2]] + a[n - a[n-3]]]; Array[a, 83] (* Giovanni Resta, Dec 13 2017 *)

PARI

my(q=vector(100)); q[1]=2;q[2]=3;q[3]=3;q[4]=4;q[5]=6;q[6]=6; for(n=7, #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 (A296440 n) (cond ((= 1 n) 2) ((<= n 3) 3) ((= 4 n) 4) ((<= n 6) 6) (else (+ (A296440 (- n (A296440 (- n 1)))) (A296440 (- n (A296440 (- n 2)))) (A296440 (- n (A296440 (- n 3)))))))) ;; Antti Karttunen, Dec 13 2017